Thermal Vibration of Magnetostrictive Material in Laminated Plates by the GDQ Method


 Bethany Pitts
 1 years ago
 Views:
Transcription
1 The Open echanics Journal, 007, 1, Thermal Vibration of agnetostrictive aterial in Laminated Plates by the GDQ ethod C.C. Hong * Department of echanical Engineering, Hsiuping Institute of Technology, Taichung, 41 Taiwan, ROC Abstract: The study of magnetostrictive material in laminated plate under thermal vibration is calculated by using the generalized differential quadrature (GDQ) method. The YS shear deformation effect is included in the time dependent of displacement field. In the thermoelastic stressstrain relations that containing the linear temperature rise and the magnetostrictive coupling terms with velocity feedback control. We use the GDQ method to normalize and discrete the dynamic differential equations in terms of displacements and shear rotations into the form of dynamic discretized equations. Four edges of rectangular laminate with simply supported boundary conditions are considered. The time responses of thermal stresses and center displacement with and without velocity control are obtained. Keywords: agnetostrictive material, thermal vibration, generalized differential quadrature method, GDQ, shear deformation, velocity feedback control. 1. ITRODUCTIO One of the new trends of material in the mechanical engineering is the functionally gradient materials (FG). In each type of FG, there are some functional layers e.g. piezoelectric, magnetostrictive, electrostrictive, shape memory alloys, in their sections can make a controlled progressive change of smart structures [1,]. agnetostrictive materials have the agnetoelectric coupling property under the action of magnetism and mechanism. TerfenolD is one of available agnetostrictive materials, can be used usually in the sensors and actuators [3]. In 005, Lee and Reddy presented the finite element method to analyze the nonlinear response of laminated plate of agnetostrictive material under thermomechanical loading [3]. They found the temperature can decrease the amplitude and period of deflection. In 005, Pradhan presented the analytical solutions for the FG shells of embedded agnetostrictive layers under vibration [1]. It was found that the agnetostrictive layers should be placed away from the neutral plane and made thinner to get better attenuation effects. In 006, Ramirez, Heyliger and Pan present the Ritz approach to get an approximate solution for the free vibration problem of twodimensional magnetoelectroelastic laminates [4]. They obtained the elastic displacements, electric potential, and magnetic potential numerical solutions. In 004, Buchanan presented the candidate materials of multiphase magnetoelectroelastic composites [5]. They found the multiphase material properties vary depending upon the ratio of fiber material to matrix material. In 003, Hong and Jane presented the GDQ method to study the shear deformation in the thermal vibration and bending of laminated plates [6,7]. They found that the maximum deflection and interlaminar stresses at center posi *Address correspondence to this author at the Department of echanical Engineering, Hsiuping Institute of Technology, Taichung, 41 Taiwan, ROC; tion of laminate increasing with the sidetothickness ratio value decreasing. In 005, Hong et al. presented the GDQ method to study the thermal vibration of a thermal sleeve [8]. They found that the computational GDQ solutions of the natural frequency, displacement and thermal stress. In 006, Hong et al. used the GDQ method to study the piezoelectric material under mechanical and electric loads [9]. They found that the numerical GDQ solutions of stress and electric potential function for the analyses of local symmetric pressure with no overshoot and no Gibbs effect and under tractionfree boundary condition of the strip. ow it is interesting to study and find the natural frequency, displacement and thermal stress of the agnetostrictive material in laminated plates with the GDQ method.. FORULATIO.1. Displacement Field The time dependent of displacements fields are assumed in the following YS (YangorrisStavsky, 1966) form [6], which is the firstorder shear deformation theory in the linear equation: u = u 0 (x, y, + z x (x, y, v = v 0 (x, y, + z y (x, y, w = w(x, y, where u 0 and v 0 are tangential displacements, w is transverse displacement of the middleplane, x and y are the shear rotations, t is time... GDQ ethod The GDQ method was presented in 1990 by Shu and Richards [11]. The GDQ method approximates the derivative of function would be used [6] and can be restated that: the derivative of a smooth function at a discrete point in a domain can be discretized by using an approximated weighting linear sum of the function values at all the discrete points in the direction [10,11]. For example, the firstorder and the / Bentham Science Publishers Ltd.
2 30 The Open echanics Journal, 007, Volume 1 C.C. Hong secondorder derivatives of function f * (x, y) at coordinates (x i, y j ) of grid point (i, j) can be discretized by: f * A x f * i, j i,l, f * B l, j y f * i, j j,m, i,m f * A () x i, j i,l f * l, j, f * B () y i, j j,m f * i,m, f * xy i, j (m) where A i, j B f * j,m l,m (m) and B i, j () denote the weighting coefficients for the m th order derivative of the function f * (x, y) with respect to the x and y directions..3. Thermoelastic StressStrain Relations with agnetostrictive Effect We consider a homogeneous, orthotropic, rectangular laminated host plate that mounted with magnetostrictive layers under uniformly distributed loading and thermal effect. Typical threelayer laminate with upper surface magnetostrictive layer which is shown in Fig., where a and b is the length in the x, y direction of the plate, h * is the plate thickness, p 1 and p are the inplane distributed forces, q is the applied pressure load, T = T 0 (x, y, + z h T * 1 (x, y, is the temperature difference between the laminate and curing area. For simplicity, the heat conduction equation for the host laminate would be used [6]. For the plane stress in a laminated material, the inplane stresses constitute the membrance stresses, bending stresses and thermal stresses with magnetostrictive effect for the k th layer are in the following equations [3]: x y xy 0 0 e e e 36 Q 11 Q 1 Q 16 = Q 1 Q Q 6 Q 16 Q 6 Q H z x x T y y T xy xy T and the interlaminar shear stresses are calculated from the following equation: yz xz = Q 44 Q 45 Q 45 Q 55 e 14 e 4 0 e 15 e H z yz xz where x and y are the coefficients of thermal expansion, xy is the coefficient of thermal shear. Q ij is the so called transformed reduced stiffness can be in terms of the elastic stiffness of materials and can be explained more detail by Whitney [1]. x, y, xy are inplane strains and yz, xz are shear strains in terms of displacement components and shear rotation, respectively. e ij is the transformed magnetostrictive coupling moduli. H z is the magnetic field intensity, expressed in the following equation. H z (x, y, = k c I (x, y, (3) (4) Fig.. Typical threelayer laminate with magnetostrictive layers.
3 Thermal Vibration of agnetostrictive aterial in Laminated Plates by the GDQ ethod The Open echanics Journal, 007, Volume 1 31 with velocity feedback control I w (x, y, = c( where k c t is the coil constant, I (x, y, is the coil current, c( is the control gain..4. Dynamic Equilibrium Differential Equations The dynamic equilibrium differential equations in terms of displacements and shear rotations included the magnetostrictive loads are expressed in the following matrix forms [3,6,1]: A 11 A 16 A 66 A 16 A 1 + A 66 A A 16 A 1 + A 66 A 6 A 66 A 6 A A 55 A 45 A 44 B 11 B 16 B 66 B 16 B 1 B B 16 B 1 B 6 B 66 B 6 B u 0 u 0 x xy u 0 v 0 v 0 y x xy v 0 y w x B 11 B 16 B 66 B 16 B 1 B 6 B 16 B 1 B 6 B 66 B 6 B D 11 D 16 D 66 D 16 D 1 + D 66 D 6 D 16 D 1 + D 66 D 6 D 66 D 6 D x x x xy x y y x y xy y y t w xy A 55 A 45 A 45 A 44 A 55 A A 45 A t w w x x y y x y x y x y A 55 A 45 A 45 A 44 = f 1 f f 3 f 4 f I x t y t u 0 t v 0 t w t H t w y x y u 0 t v 0 t x t y t (5) where f 1,, f 5 are the expressions of thermal loads (, ), mechanical loads (p 1, p, q) and magnetostrictive loads (, ). f 1 = x x + xy y + p 1 + x x + xy y f = xy x + y y + p + xy x + y y f 3 = q f 4 = x x + xy y + x x + xy y f 5 = xy x + y y + xy x + y y h * ( y, y ) = (Q 1 h * x + Q y + Q 6 xy )(T 0, z z h T 1)dz * h * ( xy, xy ) = (Q 16 h * x + Q 6 y + Q 66 xy )(T 0, z z h T 1)dz * h * h * ( x, x ) = e 31 H z (1, z )dz ( y, y ) = e 3 H z (1, z )dz h * h * ( xy, xy ) = e 36 H z (1, z )dz h * h * h * h * (A ij, B ij, D ij ) = Q ij (1, z, z )dz, (i, j = 1,, 6) h * h * Ai * j * = k k Qi * j * dz, (i *, j * = 4,5; = 6 i *, = 6 j * ) h * h * (, H, I) = 0 (1, z, z )dz in which k, k are the shear correction coefficients, 0 is the density of ply..5. Dynamic Discretized Equations We apply the weighting coefficients of discretized equations () in the twodimensional generalized differential qradrature (GDQ) method to discrete the differential equations (5) under the vibration of time sinusoidal displacement and temperature: u = [u 0 (x, y) + z x (x, y)]sin( mn, v = [v 0 (x, y) + z y (x, y)]sin( mn w = w(x, y)sin( mn, T = [T 0 (x, y) + z h * T 1(x, y)]sin(
4 3 The Open echanics Journal, 007, Volume 1 C.C. Hong where mn is natural frequency of the plate, is frequency of applied heat flux. And the following nondimensional parameters are introduced: X = x / a, Y = y / b, U = u 0 / a, V = v 0 / b, under the vibration of time sinusoidal displacement and temperature. W = 10h * w /( x T 1 a ) We obtain the following dynamic discretized equations in matrix notation: [ A ]{ SUVW }+ [ B ]{ SSIXY }+ [ KE] { SWSI} (6) + [ FQ] { UVWSI}= { F} where { SUVW }= { A () i,l U l, j V l,m () V i,m A () i,l W l, j { SSIXY }= { A () i,l x l, j () y l, j { SWSI}= { A i,l W l, j B j,m x i,m U l,m y l,m W i,m y l, j () U i,m W l,m A () i,l V l, j () W i,m x l,m y i,m () y i,m A i,l x l, j () x i,m { UVWSI}= {U i, j V i, j W i, j x i, j y i, j { F}= {F 1 F F 3 F 4 F 5 The elements of 5 9 matrix [ A ], 5 6 matrix [ B ], 5 6 matrix [ KE] and 5 5 matrix [ FQ] are as follows: A 11 = (A 11 / a)sin( mn A 1 = (A 16 / b)sin( mn A 13 = (A 66 a / b )sin( mn A 14 = (A 16 b / a )sin( mn A 15 = [(A 1 + A 66 )/a]sin( mn A 16 = (A 6 / b)sin( mn A 17 = A 18 = A 19 A 1 = (A 16 / a)sin( mn A = [(A 1 + A 66 )/b]sin( mn A 3 = (A 6 a / b )sin( mn A 4 = (A 66 b / a )sin( mn A 5 = (A 6 / a)sin( mn A 6 = (A / b)sin( mn A 7 = A 8 = A 9 A 31 = A 3 = A 33 = A 34 = A 35 = A 36 A 37 = xt 1 10h * A 55 sin( mn A 38 = x T 1 10h * (A 45 a / b)sin( mn A 39 = xt 1 10h * (A 44 a / b )sin( mn A 41 = (B 11 / a)sin( mn A 4 = (B 16 / b)sin( mn A 43 = (B 66 a / b )sin( mn A 44 = (B 16 b / a )sin( mn A 45 = (B 1 )(1 / a)sin( mn A 46 = (B 6 / b)sin( mn A 47 = A 48 = A 49 A 51 = (B 16 / a)sin( mn A 5 = (B 1 )(1 / b)sin( mn A 53 = (B 6 a / b )sin( mn A 54 = (B 66 b / a )sin( mn A 55 = (B 6 / a)sin( mn A 56 = (B / b)sin( mn A 57 = A 58 = A 59 B 11 = (B 11 / a )sin( mn B 1 = [B 16 /(ab)]sin( mn B 13 = (B 66 / b )sin( mn B 14 = (B 16 / a )sin( mn B 15 = [(B 1 )/(ab)]sin( mn B 16 = (B 6 / b )sin( mn B 1 = (B 16 / a )sin( mn B = [(B 1 )/(ab)]sin( mn B 3 = (B 6 / b )sin( mn B 4 = (B 66 / a )sin( mn B 5 = [B 6 /(ab)]sin( mn B 6 = (B / b )sin( mn B 31 = B 3 = B 33 = B 34 = B 35 = B 36 B 41 = (D 11 / a )sin( mn B 4 = [D 16 /(ab)]sin( mn B 43 = (D 66 / b )sin( mn B 44 = (D 16 / a )sin( mn B 45 = [(D 1 + D 66 )/(ab)]sin( mn B 46 = (D 6 / b )sin( mn B 51 = (D 16 / a )sin( mn B 5 = [(D 1 + D 66 )/(ab)]sin( mn B 53 = (D 6 / b )sin( mn B 54 = (D 66 / a )sin( mn B 55 = [D 6 /(ab)]sin( mn B 56 = (D / b )sin( mn k KE 11 = T x 1 a [ 1 10h * a k c( e c 31(z k z k1 )] mn cos( mn k KE 1 = T x 1 a [ 1 10h * b k c( e c 36(z k z k1 )] mn cos( mn KE 13 = KE 14 = KE 15 = KE 16
5 Thermal Vibration of agnetostrictive aterial in Laminated Plates by the GDQ ethod The Open echanics Journal, 007, Volume 1 33 k KE 1 = T x 1 a [ 1 10h * a k c( e c 36(z k z k1 )] mn cos( mn k KE = T x 1 a [ 1 10h * b k c( e c 3(z k z k1 )] mn cos( mn KE 3 = KE 4 = KE 5 = KE 6 KE 31 = KE 3 KE 33 = (A 55 / a)sin( mn KE 34 = (A 45 / b)sin( mn KE 35 = (A 45 / a)sin( mn KE 36 = (A 44 / b)sin( mn KE 41 = xt 1 10h * A 55 a sin( mn T x 1 a [ 1 10h * a k c( 1 c 3 k e 31 KE 4 = xt 1 10h * (A 45 a / b)sin( mn T x 1 a [ 1 10h * b k c( 1 c 3 k e 36 KE 43 = KE 44 = KE 45 = KE 46 KE 51 = xt 1 10h * A 45 a sin( mn T x 1 a [ 1 10h * a k c( 1 c 3 k e 36 KE 5 = x T 1 10h * (A 44 a / b)sin( mn T x 1 a [ 1 10h * b k c( 1 c 3 k e 3 KE 53 = KE 54 = KE 55 = KE 56 z 3 3 k z k1 ] h * mn cos( mn z 3 3 k z k1 ] h * mn cos( mn z 3 3 k z k1 ] h * mn cos( mn z 3 3 k z k1 ] h * mn cos( mn FQ 11 = mn a sin( mn FQ 1 = FQ 13 = FQ 15 FQ 14 = H mn sin( mn FQ = mn b sin( mn FQ 5 = H mn sin( mn FQ 1 = FQ 3 = FQ 4 FQ 31 = FQ 3 = FQ 34 = FQ 35 FQ 33 = mn [ x T 1 a /(10h * )]sin( mn FQ 41 = H mn a sin( mn FQ 4 = FQ 43 FQ 44 = (A 55 +I mn )sin( mn FQ 45 = A 45 sin( mn FQ 51 = FQ 53 FQ 5 = H mn b sin( mn FQ 54 = A 45 sin( mn FQ 55 = (A 44 + I mn )sin( mn in which F 1,..., F 5 are represented in the following discretized equation: F 1 = ( 1 a F = ( 1 a F 3 = q i, j F 4 = ( 1 a xl, j + 1 b xyi,m )sin( + p 1i, j xyl, j + 1 yi,m + p i, b j )sin( xl, j + 1 xyi,m )sin( b F 5 = ( 1 xyl, a j + 1 yi,m )sin( b in which p 1 and p are the inplane distributed forces, q is the applied pressure load. The force resultants x, xy, y and moment resultants x, xy, y are expressed as follows: T T T T T x = x, xy = xy, y = y, x = x, xy = xy, T y = y in which { T } is the thermal force resultant, { T } is the thermal moment resultant. 3. SOE UERICAL RESULTS AD DISCUS SIOS We consider the crossply laminates including shear deformation under four sides simply supported. The elastic modules of the typical host material and TerfenolD magnetostrictive material are listed in the following Table 1 [3,6]. The value of shear correction coefficient is K K = 5/6. For the simplification the typical host material conductivity Btu /(sin F), specific heat C v.16 Btu /(lbm F) are used to calculate K = /(C v ) value, and find some of the lowest frequency of applied heat flux and vibration frequency 11 of plate, Table 1. aterial Properties of Typical Host and TerfenolD aterial E 1 E G 1 E G 3 E G 1 E 1 (lb / in 3 ) x (1 / F) y (1 / F) Typical Host TerfenolD
6 34 The Open echanics Journal, 007, Volume 1 C.C. Hong at time t =0.003s, 1s, s,, 9s, for a / b = 1, threelayer (0 m /90 /0 ) laminate as shown in Fig. (). vibration of sinusoidal temperature only ( T 0, T 1 = 1.0 F, p 1 = p = q ) at time 6sec, m = n = 1 mode shape, with k c c( = 10 8, aspect ratio a / b.5, 1.0, and.0, sidetothickness ratio a / h * =100, 50, 0, 10 and 5. Fig. (3) shows that W (a /,b /) in the grid point = 9 9, and of GDQ method for the upper surface magnetostrictive layer of the threelayer (0 m /90 /0 ) We find that W (a /,b /) is in good convergence in grid point = Fig. (a). The lowest frequency of threelayer (0 m /90 /0 ) laminate. Fig. (3a). Convergence for a / b.5, threelayer (0 m /90 /0 ) Fig. (b). The lowest vibration frequency 11 of threelayer (0 m /90 /0 ) laminate. The magnetostrictive coupling moduli is e 31 = e 3 = E m d m and E m = 6.5GPa, d m = ma 1 for TerfenolD. We use the following coordinates for the grid points: x i.5[1 cos( i 1 )]a,i = 1,,..., 1 y j.5[1 cos( j 1 )]b, j = 1,,..., (7) 1 Firstly, we make the studies of dynamic convergence of center deflection amplitude W (a /,b /) in the thermal Fig. (3b). Convergence for a / b = 1.0, threelayer (0 m /90 /0 ) Fig. (4) shows that W (a /,b /) in the grid point = 9 9, and of GDQ method for the upper and lower surface magnetostrictive layers of the ten
7 Thermal Vibration of agnetostrictive aterial in Laminated Plates by the GDQ ethod The Open echanics Journal, 007, Volume 1 35 layer (0 m /90 /0 /90 /0 ) s symmetrical The superscript of m denotes magnetostrictive layer, the subscript s denotes the symmetric of laminate. We find that the 1313 grid point have the convergence result and used further in the GDQ analyses of time responses for deflection and stress. We used the k c c( values to control and reduce the amplitude of center deflection W (a /,b /). Fig. (4c). Convergence for a / b =.0, (0 m /90 /0 /90 /0 ) s Figs. (5,6) show that the k c c( values with time for thick laminated plate ah * = 10 and thin laminated ah * = 100, in threelayer and tenlayer magnetostrictive layer of laminate, respectively. Fig. (3c). Convergence for a / b =.0, threelayer (0 m /90 /0 ) Fig. (5). k c c( values vs time t (sec) in (0 m /90 /0 ) laminated plate. Fig. (4a). Convergence for a / b.5, (0 m /90 /0 /90 /0 ) s Fig. (6). k c c( values vs time t (sec) in (0 m /90 /0 /90 /0 ) s Fig. (4b). Convergence for a / b = 1.0, (0 m /90 /0 /90 /0 ) s Fig. (7) shows that time response of the nondimensional transverse center deflection amplitude W (a /,b /) with and without k c c( values at ah * = 10 and ah * = 100, respectively, for threelayer (0 m /90 /0 ) laminated plate, ab= 1, = 13 13, m = 1, n = 1, q, T 1 = 1, p 1 = p under shear effect. We find that the values of the center deflection amplitude W (a /,b /) with k c c(
8 36 The Open echanics Journal, 007, Volume 1 C.C. Hong are smaller than the values of W (a /,b /) without k c c(. The amplitude W (a /,b /) can be controlled and adjusted to a desired smaller value by using a suitable k c c( value, especially at time 0.003s, 1.s, 5.9s and 8.8s in Fig. (7a) with thick plate ah * = 10 of the GDQ method. But in Fig. (7b) with thin plate ah * = 100 of the GDQ method, the variations are small, except at time 0.003s and 0.8s. Fig. (9) shows that time response of the nondimensional transverse center deflection amplitude W (a /,b /) with and without k c c( values at ah * = 10 and ah * = 100, respectively, for tenlayer (0 m /90 /0 /90 /0 ) s symmetric laminate, ab= 1, = 13 13, m = 1, n = 1, q, T 1 = 1, p 1 = p under shear effect. We find that the values of the center deflection amplitude W (a /,b /) with k c c( are smaller than the values of W (a /,b /) without k c c(. The amplitude W (a /,b /) can be controlled and adjusted to a desired smaller value by using a suitable k c c( value, especially at time 0.003s,.6s, 5.s and 7.8s in Fig. (9a) with thick plate ah * = 10 of the GDQ method. But in Fig. (9b) with thin plate ah * = 100 of the GDQ method, the variations are small, except at time 5.1s. Fig. (7a). Thick, threelayer laminated magnetostrictive plate. Fig. (8a). Thick, threelayer laminated magnetostrictive plate. Fig. (7b). Thin, threelayer laminated magnetostrictive plate. Fig. (8). shows that time response of the dominated nondimensional stress x = x h * / ( x T 1 ae ) at center position of lower surface Z.5h * with and without k c c( values as the analyses of deflection W (a /,b /) at ah * = 10 and ah * = 100, respectively, for threelayer (0 m /90 /0 ) laminate, ab= 1, = 13 13, m = 1, n = 1, q, T 1 = 1, p 1 = p under shear effect. We find that the amplitudes of the stress x do not become the smaller values under the controlled W (a /,b /) condition in Fig. (8a) with plate ah * = 10 of GDQ method. But in Fig. (8b) with thin plate ah * = 100 of the GDQ method, the variations are small. Fig. (8b). Thin, threelayer laminated magnetostrictive plate. Fig. (9a). Thick, tenlayer laminated magnetostrictive plate.
9 Thermal Vibration of agnetostrictive aterial in Laminated Plates by the GDQ ethod The Open echanics Journal, 007, Volume 1 37 Fig. (9b). Thin, tenlayer laminated magnetostrictive plate. Fig. (10) shows that time response of the dominated nondimensional stress y = y h * / ( x TaE ) at center position of lower surface Z.5h * with and without k c c( values as the analyses of deflection W (a /,b /) at ah * = 10 and ah * = 100, respectively, for tenlayer (0 m /90 /0 /90 /0 ) s symmetric laminate, ab= 1, = 13 13, m = 1, n = 1, q, T 1 = 1, p 1 = p under shear effect. We find that the amplitudes of the stress y are almost the same value in controlled and uncontrolled W (a /,b /) condition of thick plate ah * = 10 and thin plate ah * = 100 by the GDQ method. Fig. (10a). thick, tenlayer laminated magnetostrictive plate. Fig. (10b). Thin, tenlayer laminated magnetostrictive plate. 4. COCLUSIOS (a) The numerical GDQ calculations provides an efficient method to compute the deflection and stress in the cross ply laminated plate with magnetostrictive layer subjected to thermal vibration of sinusoidal temperature including shear deformation. (b) The amplitude of transverse center deflection W (a /,b /) can be controlled to a smaller desirable value with suitable velocity feedback gain k c c( value, especially in the thick plate ah * = 10 by using the GDQ method. (c) The amplitude of the dominated stress x is not become a smaller values under the corresponding controlled W (a /,b /) condition for threelayer (0 m /90 /0 ) laminate in the thick plate ah * = 10 of the GDQ method. But the amplitudes of the dominated stress y are almost the same value in the corresponding controlled and uncontrolled W (a /,b /) condition for tenlayer (0 m /90 /0 /90 /0 ) s symmetric laminate of the GDQ method. (d) The GDQ method provide the less grid points ( = 13 13) and less computational time to get the numerical solutions of deflection and stress for magnetostrictive layer laminates. ACKOWLEDGEETS The completion of this study was made possible by a grant SC951E from ational Science Council, Taiwan, ROC. REFERECES [1] Pradhan SC. Vibration suppression of FG shells using embedded magnetostrictive layers. Int J Solids Struct 005; 4: [] Wojciechowski S. ew trends in the development of mechanical engineering materials. J ater Process Tech 000; 106: [3] Lee SJ, Reddy J. onlinear response of laminated composite plates under thermomechanical loading. Int J onlinear ech 005; 40: [4] Ramirez F, Heyliger PR, Pan E. Free vibration response of twodimensional magnetoelectroelastic laminated plates. J Sound Vibrat 006; 9: [5] Buchanan GR. Layered versus multiphase magnetoelectroelastic composites. Composites Part B. Eng 004; 35: [6] Hong CC, Jane KC, Shear deformation in thermal bending analysis of laminated plates by the GDQ method. ech Res Commun 003; 30: [7] Hong CC, Liao HW, Lee LT, Ke JB, Jane KC, Thermally induced vibration of a thermal sleeve with the GDQ method. Int J ech Sci 005; 47: [8] Hong CC, Liao HW, Lee LT, Ke JB, Jane KC, Thermally induced vibration of a thermal sleeve with the GDQ method. Int J ech Sci 005; 47: [9] Hong CC, Liao HW, Jane KC. umerical analyses of piezoelectric materials with the GDQ method. Comput at Sci 006; 35: [10] Bert CW, Jang SK, Striz AG. onlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature. Comput ech 1989; 5: [11] Shu C, Du H. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analyses of beams and plates. Int J Solds Struct 1997; 34: [1] Whitney J. Structural analysis of laminated anisotropic plates. Lancaster, PA, USA: Technomic Publishing Company, Inc., Received: July 7, 007 Revised: August 3, 007 Accepted: August 9, 007
HIGHERORDER THEORIES
HIGHERORDER THEORIES THIRDORDER SHEAR DEFORMATION PLATE THEORY LAYERWISE LAMINATE THEORY J.N. Reddy 1 ThirdOrder Shear Deformation Plate Theory Assumed Displacement Field µ u(x y z t) u 0 (x y t) +
More informationPiezoelectric Control of Multifunctional Composite Shells Subjected to an Electromagnetic Field
Piezoelectric Control of Multifunctional Composite Shells Subjected to an Electromagnetic Field *SangYun Park 1) and Ohseop Song 2) 1), 2) Department of Mechanical Engineering, Chungnam National University,
More informationEffect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Effect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure To cite this article:
More informationLaminated Composite Plates and Shells
Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer Table of Contents 1. Introduction to Composite Materials 1 1.1 Introduction 1 1.2 Classification of Composite Materials
More informationThermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature
Steel and Composite Structures, Vol. 12, No. 2 (2012) 129147 129 hermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature S. Moradi 1 and Mohammad Hassan Mansouri
More informationHIGHERORDER THEORIES
HIGHERORDER THEORIES Thirdorder Shear Deformation Plate Theory Displacement and strain fields Equations of motion Navier s solution for bending Layerwise Laminate Theory Interlaminar stress and strain
More informationBending of Simply Supported Isotropic and Composite Laminate Plates
Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto GutierrezMiravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,
More informationAnalysis of NonRectangular Laminated Anisotropic Plates by Chebyshev Collocation Method
146 Analysis of NonRectangular Laminated Anisotropic Plates by Chebyshev Collocation Method ChihHsun LIN and MingHwa R. JEN The purpose of this work is to solve the governing differential equations
More informationDynamic Analysis of Laminated Composite Plate Structure with Square CutOut under Hygrothermal Load
Dynamic Analysis of Laminated Composite Plate Structure with Square CutOut under Hygrothermal Load Arun Mukherjee 1, Dr. Sreyashi Das (nee Pal) 2 and Dr. A. Guha Niyogi 3 1 PG student, 2 Asst. Professor,
More information(This is a sample cover image for this issue. The actual cover is not yet available at this time.)
(This is a sample cover image for this issue. The actual cover is not yet available at this time. This article appeared in a journal published by Elsevier. The attached copy is furnished to the author
More informationVIBRATION CONTROL OF RECTANGULAR CROSSPLY FRP PLATES USING PZT MATERIALS
Journal of Engineering Science and Technology Vol. 12, No. 12 (217) 33983411 School of Engineering, Taylor s University VIBRATION CONTROL OF RECTANGULAR CROSSPLY FRP PLATES USING PZT MATERIALS DILEEP
More informationFREE VIBRATION OF THERMALLY PRE/POSTBUCKLED CIRCULAR THIN PLATES EMBEDDED WITH SHAPE MEMORY ALLOY FIBERS
Journal of Thermal Stresses, 33: 79 96, 2010 Copyright Taylor & Francis Group, LLC ISSN: 01495739 print/1521074x online DOI: 10.1080/01495730903409235 FREE VIBRATION OF THERMALLY PRE/POSTBUCKLED CIRCULAR
More informationInternational Journal of Advanced Engineering Technology EISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationNONLINEAR DYNAMIC ANALYSIS OF AN ORTHOTROPIC COMPOSITE ROTOR BLADE
Journal of Marine Science and Technology, Vol., o. 4, pp. 4755 (4) 47 OIEAR DYAMIC AAYSIS OF A ORTHOTROPIC COMPOSITE ROTOR BADE MingHung Hsu Key words: orthotropic composite rotor blade, differential
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of aterials Science and Engineering A 6 (12) (2016) 3542 doi: 10.17265/21616213/2016.12.005 D DAVID PUBLISHIG Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K
More informationChapter 5 Elastic Strain, Deflection, and Stability 1. Elastic StressStrain Relationship
Chapter 5 Elastic Strain, Deflection, and Stability Elastic StressStrain Relationship A stress in the xdirection causes a strain in the xdirection by σ x also causes a strain in the ydirection & zdirection
More informationThermal buckling and postbuckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method
hermal buckling and postbuckling of laminated composite plates with temperature dependent properties by an asymptotic numerical method F. Abdoun a,*, L. Azrar a,b, E.M. Daya c a LAMA, Higher School of
More informationTRANSIENT ANALYSIS OF SMART MATERIAL PLATES USING HIGHER ORDER THEORY
VOL. 1, NO. 1, JANUARY 15 ISSN 1819668 615 Asian Research Publishing Network (ARPN). All rights reserved. TRANSINT ANALYSIS OF SMART MATRIAL PLATS USING HIGHR ORDR THORY P. Ravikanth Raju 1, J. Suresh
More informationVIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS
VIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS Mechanical Engineering Department, Indian Institute of Technology, New Delhi 110 016, India (Received 22 January 1992,
More informationStatic and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method
8(2011) 463 472 Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method Abstract Static and free vibration analysis of carbon nano wires
More informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: ModeSuperposition Method ModeSuperposition Method:
More informationFLEXURAL RESPONSE OF FIBER RENFORCED PLASTIC DECKS USING HIGHERORDER SHEAR DEFORMABLE PLATE THEORY
AsiaPacific Conference on FRP in Structures (APFIS 2007) S.T. Smith (ed) 2007 International Institute for FRP in Construction FLEXURAL RESPONSE OF FIBER RENFORCED PLASTIC DECKS USING HIGHERORDER SHEAR
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationAnalysis of Cylindrical Shells Using Generalized Differential Quadrature
C. T. Loy K. Y. Lam C. Shu Department of Mechanical and Production Engineering ational University of Singapore 10 Kent Ridge Crescent Singapore 0511 Analysis of Cylindrical Shells Using Generalized Differential
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationApplication of piezoelectric actuators to active control of composite spherical caps
Smart Mater. Struct. 8 (1999 18. Printed in the UK PII: S964176(9916614 Application of piezoelectric actuators to active control of composite spherical caps Victor Birman, Gareth J Knowles and John J
More informationModule 6: Smart Materials & Smart Structural Control Lecture 33: Piezoelectric & Magnetostrictive Sensors and Actuators. The Lecture Contains:
The Lecture Contains: Piezoelectric Sensors and Actuators Magnetostrictive Sensors and Actuators file:///d /chitra/vibration_upload/lecture33/33_1.htm[6/25/2012 12:42:09 PM] Piezoelectric Sensors and Actuators
More informationFree vibration analysis of elastically connected multiplebeams with general boundary conditions using improved Fourier series method
Free vibration analysis of elastically connected multiplebeams with general boundary conditions using improved Fourier series method Jingtao DU*; Deshui XU; Yufei ZHANG; Tiejun YANG; Zhigang LIU College
More informationThermal deformation compensation of a composite beam using piezoelectric actuators
INSTITUTE OF PHYSICS PUBLISHING Smart Mater. Struct. 13 (24) 3 37 SMART MATERIALS AND STRUCTURES PII: S9641726(4)79738 Thermal deformation compensation of a composite beam using piezoelectric actuators
More informationCalculation of Energy Release Rate in Mode I Delamination of Angle Ply Laminated Composites
Copyright c 2007 ICCES ICCES, vol.1, no.2, pp.6167, 2007 Calculation of Energy Release Rate in Mode I Delamination of Angle Ply Laminated Composites K. Gordnian 1, H. Hadavinia 1, G. Simpson 1 and A.
More informationFree Vibration Response of a Multilayer Smart Hybrid Composite Plate with Embedded SMA Wires
11(2014) 279298 Free Vibration Response of a Multilayer Smart Hybrid Composite Plate with Embedded SMA Wires Abstract In this paper, free vibration response of a hybrid composite plate was studied. Effects
More informationComposites Design and Analysis. Stress Strain Relationship
Composites Design and Analysis Stress Strain Relationship Composite design and analysis Laminate Theory Manufacturing Methods Materials Composite Materials Design / Analysis Engineer Design Guidelines
More informationDYNAMIC RESPONSE OF SYNTACTIC FOAM CORE SANDWICH USING A MULTIPLE SCALES BASED ASYMPTOTIC METHOD
ECCM66 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 6 June 4 DYNAMIC RESPONSE OF SYNTACTIC FOAM CORE SANDWICH USING A MULTIPLE SCALES BASED ASYMPTOTIC METHOD K. V. Nagendra Gopal a*,
More informationME 7502 Lecture 2 Effective Properties of Particulate and Unidirectional Composites
ME 75 Lecture Effective Properties of Particulate and Unidirectional Composites Concepts from Elasticit Theor Statistical Homogeneit, Representative Volume Element, Composite Material Effective Stress
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationPrediction of Elastic Constants on 3D Fourdirectional Braided
Prediction of Elastic Constants on 3D Fourdirectional Braided Composites Prediction of Elastic Constants on 3D Fourdirectional Braided Composites Liang Dao Zhou 1,2,* and Zhuo Zhuang 1 1 School of Aerospace,
More informationLecture 8. Stress Strain in Multidimension
Lecture 8. Stress Strain in Multidimension Module. General Field Equations General Field Equations [] Equilibrium Equations in Elastic bodies xx x y z yx zx f x 0, etc [2] Kinematics xx u x x,etc. [3]
More informationFinite Element Analysis of Piezoelectric Cantilever
Finite Element Analysis of Piezoelectric Cantilever Nitin N More Department of Mechanical Engineering K.L.E S College of Engineering and Technology, Belgaum, Karnataka, India. Abstract Energy (or power)
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of Materials Science and Engineering A 6 () 354 doi:.765/663/6..5 D DAVID PUBLISHING Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K * and V V Subba Rao Faculty
More informationbased on HBLS Smart Materials
Module 5: Sensors based on HBLS Smart Materials Bishakh Bhattacharya and Nachiketa Tiwari Dprt Department tof fmechanical lengineering Indian Institute of Technology, Kanpur Topics Covered in the Last
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationBending Analysis of Symmetrically Laminated Plates
Leonardo Journal of Sciences ISSN 15830233 Issue 16, JanuaryJune 2010 p. 105116 Bending Analysis of Symmetrically Laminated Plates Bouazza MOKHTAR 1, Hammadi FODIL 2 and Khadir MOSTAPHA 2 1 Department
More informationAN ANALYSIS OF A PIEZOELASTIC RESTRICTOR USING A CAPACITIVE SHUNT
TASK QUARTERLY 8 No 3(2004), 377 384 AN ANALYSIS OF A PIEZOELASTIC RESTRICTOR USING A CAPACITIVE SHUNT MARINOKEKANA 1 ANDJANUSZBADUR 2 1 CentreforAdvancedMaterials,DesignandManufacturingResearch, Durban
More informationThe Rotating Inhomogeneous Elastic Cylinders of. VariableThickness and Density
Applied Mathematics & Information Sciences 23 2008, 237 257 An International Journal c 2008 Dixie W Publishing Corporation, U. S. A. The Rotating Inhomogeneous Elastic Cylinders of VariableThickness and
More informationVIBRATION CONTROL SIMULATION OF LAMINATED COMPOSITE PLATES WITH INTEGRATED PIEZOELECTRICS
Journal of Sound and Vibration (999) 22(5), 827 846 Article No. jsvi.998.97, available online at http://www.idealibrary.com.on VIBRATION CONTROL SIMULATION OF LAMINATED COMPOSITE PLATES WITH INTEGRATED
More informationEFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING
Journal of MECHANICAL ENGINEERING Strojnícky časopis, VOL 67 (217), NO 1, 522 EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Arnab Choudhury 1,
More informationChapter 2 Buckling and Postbuckling of Beams
Chapter Buckling and Postbuckling of Beams Abstract This chapter presents buckling and postbuckling analysis of straight beams under thermal and mechanical loads. The Euler and Timoshenko beam theories
More informationThreedimensional thermoelastic deformations of a functionally graded elliptic plate
JCOMB Composites: Part B () 9 6 www.elsevier.com/locate/compositesb Threedimensional thermoelastic deformations of a functionally graded elliptic plate Z.Q. Cheng a, R.C. Batra b, * a Department of Modern
More informationFinite Element and Plate Theory Modeling of Acoustic Emission Waveforms. NASA Langley Research Center. Hampton, VA *University of Denver
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms W. H. Prosser, M. A. Hamstad + *, J. Gary +, and A. O Gallagher + NASA Langley Research Center Hampton, VA 236811 *University of
More informationMODIFIED HYPERBOLIC SHEAR DEFORMATION THEORY FOR STATIC FLEXURE ANALYSIS OF THICK ISOTROPIC BEAM
MODIFIED HYPERBOLIC SHEAR DEFORMATION THEORY FOR STATIC FLEXURE ANALYSIS OF THICK ISOTROPIC BEAM S. Jasotharan * and I.R.A. Weerasekera University of Moratuwa, Moratuwa, Sri Lanka * EMail: jasos91@hotmail.com,
More informationA two variable refined plate theory for orthotropic plate analysis
A two variable refined plate theory for orthotropic plate analysis R.P. Shimpi *, H.G. Patel Department of Aerospace Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra,
More informationMAGNETOELECTROELASTIC laminates possess coupled
Twodimensional Static Fields in Magnetoelectroelastic Laminates* PAUL R. HEYLIGER, 1,y FERNANDO RAMIRE 1 AND ERNIAN PAN 2 1 Department of Civil Engineering, Colorado State University, Fort Collins, CO
More informationAnalysis of laminated composite skew shells using higher order shear deformation theory
10(2013) 891 919 Analysis of laminated composite skew shells using higher order shear deformation theory Abstract Static analysis of skew composite shells is presented by developing a C 0 finite element
More informationGeneric Strategies to Implement Material Grading in Finite Element Methods for Isotropic and Anisotropic Materials
University of Nebraska  Lincoln DigitalCommons@University of Nebraska  Lincoln Engineering Mechanics Dissertations & Theses Mechanical & Materials Engineering, Department of Winter 1292011 Generic
More informationPIEZOELECTRIC TECHNOLOGY PRIMER
PIEZOELECTRIC TECHNOLOGY PRIMER James R. Phillips Sr. Member of Technical Staff CTS Wireless Components 4800 Alameda Blvd. N.E. Albuquerque, New Mexico 87113 Piezoelectricity The piezoelectric effect is
More informationThe New Boundary Condition Effect on The Free Vibration Analysis of Microbeams Based on The Modified Couple Stress Theory
International Research Journal of Applied and Basic Sciences 2015 Available online at www.irjabs.com ISSN 2251838X / Vol, 9 (3): 274279 Science Explorer Publications The New Boundary Condition Effect
More informationStability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using SplineFSM
528 Stability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using SplineFSM Abstract The dynamic behavior of variable stiffness composite laminated (VSCL) plate with curvilinear
More informationVibroacoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai Huang1, *
3rd International Conference on Materials Engineering, Manufacturing Technology and Control (ICMEMTC 2016) Vibroacoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai
More information%&'( )'(* +,+ &(. /0(1 (2 3 * &+78 (4 3', 9:4'
!" 9 44 69 %&''(* +,+ &(. /( ( * ++4 56+ &+78 (4 ', 9:4' ;< =4 * )(>*/? A* ) B 9: ' 8 4 '5 *6 &7, &. % / + % & % '*!" #$ C )* &%E.@ ; D BC &' 8 ; & %  ;% ;< &= > &=.@ A @*". ' +. ; %. '(. 7 / %.@
More informationHybridinterface finite element for laminated composite and sandwich beams
Hybridinterface finite element for laminated composite and sandwich beams A.N. Bambole, Y.M. Desai Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
More informationVibration Analysis of Isotropic and Orthotropic Plates with Mixed Boundary Conditions
Tamkang Journal of Science and Engineering, Vol. 6, No. 4, pp. 76 (003) 7 Vibration Analsis of Isotropic and Orthotropic Plates with Mied Boundar Conditions MingHung Hsu epartment of Electronic Engineering
More informationFree Vibration Analysis of Functionally Graded Material Plates with Various Types of Cutouts using Finite Element Method
International Journal of Current Engineering and Technology EISSN 2277 4106, PISSN 2347 5161 2018 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Free
More informationCOMPARISON OF PLATE MODELS FOR ANALYSIS OF LAMINATED COMPOSITES
COMPARISON OF PLATE MODELS FOR ANALYSIS OF LAMINATED COMPOSITES P. M. Mohite and C. S. Upadhyay** Department of Aerospace Engineering, IIT Kanpur 0806, INDIA, email: mohite@iitk.ac.in Assistant Professor,
More informationMECHANICS OF MATERIALS
CHATR Stress MCHANICS OF MATRIALS and Strain Axial Loading Stress & Strain: Axial Loading Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced
More informationChapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements
CIVL 7/8117 Chapter 12  Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness
More informationUsing MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,
Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business
More informationAccepted Manuscript. R.C. Batra, J. Xiao S (12) Reference: COST Composite Structures. To appear in:
Accepted Manuscript Finite deformations of curved laminated St. VenantKirchhoff beam using layerwise third order shear and normal deformable beam theory (TSNDT) R.C. Batra, J. Xiao PII: S02638223(12)004862
More informationA coupled field finite element model to predict actuation properties of piezoelectrically actuated bistable composites.
A coupled field finite element model to predict actuation properties of piezoelectrically actuated bistable composites. P.F.Giddings, C.R.Bowen, H.A.Kim University of Bath, UK Dept. Mech. ng, University
More informationFree vibration analysis of beams by using a thirdorder shear deformation theory
Sādhanā Vol. 32, Part 3, June 2007, pp. 167 179. Printed in India Free vibration analysis of beams by using a thirdorder shear deformation theory MESUT ŞİMŞEK and TURGUT KOCTÜRK Department of Civil Engineering,
More informationShape Control of Composite Structures with Optimally Placed Piezoelectric Patches
Shape Control of Composite Structures with Optimally Placed Piezoelectric Patches by Ramesh Periasamy A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree
More informationABHELSINKI UNIVERSITY OF TECHNOLOGY
ABHELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D HELSINKI A posteriori error analysis for the Morley plate element Jarkko Niiranen Department of Structural
More informationMIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING
144 MIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING J. N. Reddy* and ChenShyhTsay School of Aerospace, Mechanical and Nuclear Engineering, University of Oklahoma, Norman, Oklahoma The paper describes
More informationLaminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change
United States Department of Agriculture Forest Service Forest Products Laboratory Research Paper FPL 375 June 1980 Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change
More informationModeling of induced strain actuation of shell structures
Modeling of induced strain actuation of shell structures Zaffir Chaudhry, Frederic Lalande, and Craig A. Rogers Center for Intelligent Material Systems and Structures, Virginia Polytechnic Institute and
More informationA Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core
Commun. Theor. Phys. 56 774 778 Vol. 56, No. 4, October 5, A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core JIANG
More informationMahdi Adineh & Mehran Kadkhodayan
Threedimensional thermoelastic analysis of multidirectional functionally graded rectangular plates on elastic foundation Mahdi Adineh & Mehran Kadkhodayan Acta Mechanica ISSN 00015970 Volume 228 Number
More informationTemperature Dependent and Independent Material Properties of FGM Plates
Temperature Dependent and Independent Material Properties of FGM Plates K. Swaminathan 1, D. M. Sangeetha 2 1,2 (Department of Civil Engineering, National Institute of Technology Karnataka, India) Abstarct:
More informationA HIGHERORDER BEAM THEORY FOR COMPOSITE BOX BEAMS
A HIGHERORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D64289 Darmstadt, Germany kroker@mechanik.tudarmstadt.de,
More informationBuckling Analysis of RingStiffened Laminated Composite Cylindrical Shells by FourierExpansion Based Differential Quadrature Method
Applied Mechanics and Materials Vol. 225 (2012) pp 207212 (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/amm.225.207 Buckling Analysis of RingStiffened Laminated Composite
More informationMechanics Research Communications
Mechanics Research Communications 85 (27) 5 Contents lists available at ScienceDirect Mechanics Research Communications journal h om epa ge: www.elsevier.com/locate/mechrescom Load s temporal characteristics
More information2766. Differential quadrature method (DQM) for studying initial imperfection effects and pre and postbuckling vibration of plates
2766. Differential quadrature method (DQM) for studying initial imperfection effects and pre and postbuckling vibration of plates Hesam Makvandi 1, Shapour Moradi 2, Davood Poorveis 3, Kourosh Heidari
More informationTABLE OF CONTENTS. Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA
Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA TABLE OF CONTENTS 1. INTRODUCTION TO COMPOSITE MATERIALS 1.1 Introduction... 1.2 Classification... 1.2.1
More informationNonlinear bending analysis of laminated composite stiffened plates
Nonlinear bending analysis of laminated composite stiffened plates * S.N.Patel 1) 1) Dept. of Civi Engineering, BITS Pilani, Pilani Campus, Pilani333031, (Raj), India 1) shuvendu@pilani.bitspilani.ac.in
More informationANALYSIS OF YARN BENDING BEHAVIOUR
ANALYSIS OF YARN BENDING BEHAVIOUR B. Cornelissen, R. Akkerman Faculty of Engineering Technology, University of Twente Drienerlolaan 5, P.O. Box 217; 7500 AE Enschede, the Netherlands b.cornelissen@utwente.nl
More informationDynamic Stability of Laminated Composite Plates with an External Smart Damper
Journal of Solid Mechanics Vol. 8, No. 1 (2016) pp. 4557 Dynamic Stability of Laminated Composite Plates with an External Smart Damper M. Hoseinzadeh, J. Rezaeepazhand * Department of Mechanical Engineering,
More informationAvailable online at ScienceDirect. C. H. Jiang, T. Y. Kam*
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 67 ( 013 ) 545 558 7th AsianPacific Conference on Aerospace Technology and Science, 7th APCATS 013 Vibration analysis of elastically
More informationDifferential Quadrature Method for Solving Hyperbolic Heat Conduction Problems
Tamkang Journal of Science and Engineering, Vol. 12, No. 3, pp. 331 338 (2009) 331 Differential Quadrature Method for Solving Hyperbolic Heat Conduction Problems MingHung Hsu Department of Electrical
More informationFlexural Analysis of Deep Aluminum Beam
Journal of Soft Computing in Civil Engineering 1 (018) 7184 journal homepage: http://www.jsoftcivil.com/ Fleural Analysis of Deep Aluminum Beam P. Kapdis 1, U. Kalwane 1, U. Salunkhe 1 and A. Dahake
More informationShishir Kumar Sahu, Ph. D. Professor Civil Engineering Department National Institute of Technology, Rourkela Orissa, India
Shishir Kumar Sahu, Ph. D. Professor Civil Engineering Department National Institute of Technology, Rourkela Orissa, India Introduction Review Of Literature Aim & Scope Of Present Investigation Finite
More informationUnit 13 Review of Simple Beam Theory
MIT  16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 1015 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics
More informationTransactions on Modelling and Simulation vol 9, 1995 WIT Press, ISSN X
An alternative boundary element formulation for plate bending analysis J.B. Paiva, L.O. Neto Structures Department, Sao Carlos Civil Engineering School, f, BrazzY Abstract This work presents an alternative
More informationTHE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE
Journal of Applied Mathematics and Computational Mechanics 013, 1(4), 131 THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE Jolanta Błaszczuk
More informationSymmetric Bending of Beams
Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications
More informationModule III  Macromechanics of Lamina. Lecture 23. MacroMechanics of Lamina
Module III  Macromechanics of Lamina Lecture 23 MacroMechanics of Lamina For better understanding of the macromechanics of lamina, the knowledge of the material properties in essential. Therefore, the
More informationHygrothermal stresses in laminates
Hygrothermal stresses in laminates Changing environment conditions (temperature and moisture) have an important effect on the properties which are matrix dominated. Change in temperaturet and moisture
More informationCHAPTER 5. Beam Theory
CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The EulerBernoulli assumptions One of its dimensions
More informationCitation Composite Structures, 2000, v. 50 n. 2, p
Title Predictorcorrector procedures for analysis of laminated plates using standard Mindlin finite element models Author(s) Sze, KY; He, LW; Cheung, YK Citation Composite Structures, 000, v. 50 n., p.
More informationNonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory
Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory TaiPing Chang 1 and QueyJen Yeh 1 Department of Construction Engineering, National Kaohsiung First
More informationAdvanced Vibrations. DistributedParameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian
Advanced Vibrations DistributedParameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir DistributedParameter Systems: Exact Solutions Relation between Discrete and Distributed
More informationSmallScale Effect on the Static Deflection of a Clamped Graphene Sheet
Copyright 05 Tech Science Press CMC, vol.8, no., pp.037, 05 SmallScale Effect on the Static Deflection of a Clamped Graphene Sheet G. Q. Xie, J. P. Wang, Q. L. Zhang Abstract: Smallscale effect on the
More information