omenclature a b c f h Length of the panel between the supports Width of the panel between the supports/ width of the beam Sandwich beam/ panel core thickness Thickness of the panel face sheet Sandwich beam/ panel overall thickness m, n umber of terms in double Fourier series p(x,y) p 2k+1, q 2k+1 p 2k+1 *, q 2k+1 * p mn q mn, q mn * r mn, r mn * t u v w w b w s w b * w s * Pressure in xy-plane expressed in double Fourier series Constants used in the shear load equations before core Constants used in the shear load equations after core Unknown coefficient for pressure Unknown coefficient for bending deflection before and after core Unknown coefficient for shear deflection before and after core Thickness of the beam face sheet In-plane displacement of the panel parallel to x-axis In-plane displacement of the panel parallel to y-axis Out-of-plane displacement of the panel parallel to z-axis Beam/ panel deflection due to bending before core Beam/ panel deflection due to shear before core Beam/ panel deflection due to bending after core Beam/ panel deflection due to shear after core xv
A eff B B f Effective contact area of the bladder with the panel Bending rigidity of sandwich structure about its mid-plane Bending rigidity of beam face sheet about its own neutral axis C 1 D D 1, D 2, D 3 D xf, D yf Constant used in bending moment equations Flexural rigidity of the panel face sheet E 1 E c E c0 E c1 E f Modulus of elasticity of core Modulus of elasticity of core before Modulus of elasticity of core after Modulus of elasticity of face sheet F 1, F 2, F 3 F L G c, G f G c0 G c1 Load measured by the load cell Shear modulus of core and face sheet respectively Shear modulus of core before Shear modulus of core after H 1, H 2, H 3 I J K K pl L Constant used in shear stress equations Constant determined by the face sheet and core thickness Constant used in shear force equations Material parameter for bi-linear material model Distance between the support rollers xvi
L* Total length of sandwich beam M (1) M xf (2) M xf M x, M y M xtot, M ytot M xy, M yx M xytot, M yxtot Bending moment Moment on the face sheets due to loading Moment of the face sheets due to the bending about its own midplanes Bending moments in the panel per unit length/ width before core Total bending moments in the panel per unit length/ width after core Twisting moments in the panel per unit width before core Total twisting moments in the panel per unit width after core BF ormal/ membrane load in bottom face sheet TF ormal/ membrane load in top face sheet BF ( Xg ) Global X-axis component of the bottom face sheet membrane force BF(Yg) Global Y-axis component of the bottom face sheet membrane force TF ( Xg ) Global X-axis component of the top face sheet membrane force Global Y-axis component of the top face sheet membrane force x, y xy, yx P P b Q c, Q xc, Q yc Q c * ormal forces in the faces per unit length Shear forces in the faces per unit length Total load applied in four point bending Measured bladder pressure Shear load carried by the core before core Shear load carried by the core after core xvii
Q xc0 Q (1) (1) xf, Q yf Q (2) (2) xf, Q yf Q tot, Q xtot, Q ytot Q tot *, Q xtot *, Q ytot * Shear component at core initiation Shear load carried by the face sheet due to bending curvature Shear load carried by the face sheet due to shear curvature Total shear load before core Total shear load after core BF (Yg) Total resultant force in global Y-axis in bottom face sheet C(Yg) Total resultant force in global Y-axis in core Total resultant force in global Y-axis in top face sheet TOT (Yg) Total resultant force in global Y-axis for sandwich panel S, S c Shear stiffness of the core S c0 S c1 C Shear stiffness of the core before core Shear stiffness of the core after core Shear load Shear load in core BF Shear load in bottom face sheet TF Shear load in top face sheet C ( Xg ) Global X-axis component of the core shear force C(Yg) Global Y-axis component of the core shear force BF ( Xg ) Global X-axis component of the bottom face sheet shear force BF (Yg) Global Y-axis component of the bottom face sheet shear force TF ( Xg ) Global X-axis component of the top face sheet shear force xviii
Global Y-axis component of the top face sheet shear force X G Y G Global X-axis in I-DEAS Global Y-axis in I-DEAS α, β Constants used in the double Fourier series ε x, ε y ε x *, ε y * φ γ 0 γ c γ xy γ xzc In-plane strains before core In-plane strains after core Width of the unloaded panel region Shear strain at yield Shear deformation in the beam core In-plane shear strain Core shear strain component γ xy * ϕ λ 0, λ 1 ν f σ 0 τ 0 τ xy τ xz, τ yz τ xzc, τ yzc In-plane shear strain after core Distance from the support point to the elastic/ plastic interface Constants used in shear load equations before and after core Poisson s ratio of face sheet Yield point in uniaxial tension Shear stress at the yield point In-plane shear stress Shear stress components in sandwich panel Shear stress components in core xix