Stability of Smart Beams with Varying Properties Based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

Size: px
Start display at page:

Download "Stability of Smart Beams with Varying Properties Based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation"

Transcription

1 Australian Journal of Basic and Applied Sciences, 5(7): , ISSN Stability of Smart Beams wit Varying Properties Based on te First Order Sear Deformation Teory ocated on a Continuous Elastic Foundation M. KaramiKorramabadi, A.R. Nezamabadi Department of Mecanical Engineering, Korramabad Branc, Islamic Azad University, Korramabad, Iran. Department of Mecanical Engineering, Arak Branc, Islamic Azad University, Arak, Iran. Abstract: Tis paper studies stability of functionally graded beams wit piezoelectric layers subjected to axial compressive load tat is simply supported at bot ends lies on a continuous elastic foundation. Te displacement field of beam is assumed based on first order sear deformation beam teory. Applying te Hamilton's principle, te governing equation is establised. Te influences of applied voltage, dimensionless geometrical parameter, functionally graded index, foundation coefficient and piezoelectric tickness on te critical buckling load of beam are presented. To investigate te accuracy of te present analysis, a compression study is carried out wit a known data. Key words: Mecanical Buckling, Functionally graded beam- Piezoelectric layer. INTRODUCTION Structural stability is considered to be one of te most important engineering issues in te design and application of slender structures. Buckling and postbuckling are te two main types of structural instability, tey often govern te failure of structures under static or dynamic compressive loading conditions, tus, ave been investigated by several researcers in te past decades (Ari-Gur, J., 98). Piezoelectric materials ave been used in te past few years in a variety of applications ranging from active control to noise suppression. In all tese applications, piezoelectric actuators are used to enance te performance of a structural system by inducing a favorable structural deformation. Detailed models on te iteration between piezoelectric sensors or actuators wit te structure to wic tey are bonded or embedded ave been developed (Tzou, H.S., G.C. Wan, 99). To te autor's knowledge, tere is no analytical solution available in te open literatures for stability of functionally graded beams wit piezoelectric layers located on a continuous elastic foundation based on first order sear deformation beam teory. In te present work, te stability of a functionally graded beam wit piezoelectric actuators subjected to axial compressive loads located on a continuous elastic foundation based on first order sear deformation beam teory is studied. Appling te Hamilton's principle, te equilibrium equations of beam are derived and solved. Te effects of dimensionless geometrical parameter, foundation coefficient and functionally graded index on te critical buckling load of beam are presented. To investigate te accuracy of te present analysis, a compression study is carried out wit a known data. Formulation Te formulation tat is presented ere is based on first order sear deformation beam teory. Based on tis teory, te displacement field can be written as (Wang C.M., J.N. Reddy, ): uxz (, ) z ( x), wxz (, ) w( xz, ) () In view of te displacement field, te strain displacement relations are given by (Wang C.M., J.N. Reddy, ): u d xx z, u w dw xz x dx z x dx () Corresponding Autor: M. Karami Korramabadi, Department of Mecanical Engineering, Korramabad Branc, Islamic Azad University, Korramabad, Iran. 743

2 Aust. J. Basic & Appl. Sci., 5(7): , Consider a functionally graded beam wit piezoelectric actuators and rectangular cross-section as sown in Fig.. Te tickness, lengt, and widt of te beam are denoted, respectively, by, and b. Also, T and B are te tickness of top and bottom of piezoelectric actuators, respectively. Te x-y plane coincides wit te midplane of te beam and te z-axis located along te tickness direction. Fig. : Scematic of te problem studied. Te Young's modulus E is assumed to vary as a power form of te tickness coordinate variable z (-/< z < /) as follow (Karami, 8): z Ez ( ) ( Ec Em) VEm, V k (3) were k is te power law index and te subscripts m and c refer to te metal and ceramic constituents, respectively. Te constitutive relations for functionally graded beam wit piezoelectric layers based on first order sear deformation beam teory are given by (Wang C.M., J.N. Reddy, ): Q ( z) e E, Q ( z) e E xx xx 3 z xz 55 xz 5 x (4) V were Ei and xx, xz,q ( z), Q 55( z) are te normal, sear stresses and plane stress-reduced stiffnesses and i e, e 3 5 are piezoelectric elastic stiffnesses respectively. Also, u and w are te displacement components in te x- and z- directions, respectively. Te potential energy can be expressed as (Wang C.M., J.N. Reddy, ): U ( xxxx xz xz ) d v v Substituting Eq. () and Eq. (4) into Eq. (5) and neglecting te iger-order terms, we obtain [ ( ) ( ( ) 3( T T B B) 5( T B)( ) dx dx dx dx dx b d dw dw d dw U D A e V V e V V (5) (6) T were A Q ( z)dz, D z Q( z)dz and VT, VB are te applied voltages on te top and B 55 T B bottom actuators respectively. Te beam is subjected to te axial compressive loads. Te work done by te axial compressive load can be expressed as (Wang C.M., J.N. Reddy, ): w W P dx x We apply te Hamilton's principle to derive te equilibrium equations of beam, tat is (Wang C.M., J.N. Reddy, ): (7) 744

3 Aust. J. Basic & Appl. Sci., 5(7): , t ( T U W) dt (8) Substitution from Eqs. (6) and (7) into Eq. (8) leads to te following equilibrium equations of te functionally graded Engesser-Timosenko beam wit piezoelectric layers. Assume tat a FG beam wit piezoelectric actuators tat is simply supported at bot ends lies on a continuous elastic foundation, wose reaction at every point is proportional to te deflection (Winkler foundation). Te equilibrium equation of te FG beams wit piezoelectric layers located on a continuous elastic foundation subjected to axial compressive load is obtained from equilibrium equations by te addition of ηw for te foundation reaction as dw d dw d ( PbA) ba( ) w, A( ) e 5VT D( ) dx dx dx dx (9) were η is te foundation coefficient. Stability Analysis: Te boundary conditions for te pin-ended Timosenko column are given by: dw d w, at x and x dx dx () Substituting Eq. () into (9) and by equating power-law index to zero and neglecting te piezoelectric effect and foundation coefficient, te critical Engesser-Timosenko buckling load of a omogeneous beam will be derived, tat is: p cr b Q Q (( ) ) /( ( ) ) 3 55 b Q () Te above equation as been reported by Wang and Reddy (Wang C.M., J.N. Reddy, ). Numerical Results: Te mecanical buckling beaviors of simply supported functionally graded Engesser-Timosenko beams wit piezoelectric actuators located on a continuous elastic foundation are studied in tis paper. Te material properties of te beam are listed in Table. Table : Material properties. Property Piezoelectric layer FGM layer Stainless steel Nickel Young's modulus Poisson's ratio engt Tickness.5.. Density Piezo constant Te Poisson s ratio is cosen to be.3 for bot materials. Te critical buckling loads for Bernoulli-Euler beam (BEB) and Engesser-Timosenko beam (ETB) evaluated considering of a / =., b/ =, =, V=v and several values of dimensionless geometrical parameter / are sown in Fig.. It is seen tat te critical buckling loads for Engesser-Timosenko beam are generally lower tan corresponding values of Bernoulli- Euler(Karami, 8) beam. Fig. 3 demonstrates te buckling loads for functionally graded Engesser-Timosenko beam. It is seen tat te critical buckling loads for Engesser-Timosenko beam increased wit an increase of te ratio / and decreased wit an increase of power-law index of constituent volume fraction. 745

4 Aust. J. Basic & Appl. Sci., 5(7): , Fig. : Critical Buckling oad of FG Smart Beam Versus /. Fig. 3: Critical Buckling oad of FG Smart Beam Versus / for V= v. Conclusion: Te stability of a functionally graded Engesser-Timosenko beam wit piezoelectric actuators located on a continuous elastic foundation subjected to axial compressive loads is studied. It is conclude tat:. Te piezoelectric actuators induce tensile piezoelectric force produced by applying negative voltages tat significantly affect te stability of te functionally graded Engesser-Timosenko beam wit piezoelectric actuators.. Te critical buckling loads of FG Engesser-Timosenko beam are generally lower tan corresponding values for te omogeneous Engesser-Timosenko beam. 3. Te critical buckling loads of FG Engesser-Timosenko beam under axial compressive load generally increases wit te increase of relative tickness /. 4. Te accuracy of Engesser-Timosenko beam teory is more tan Bernoulli-Euler beam teory. REFERENCES Ari-Gur, J., T. Weller, J. Singer, 98. Experimental and teoretical studies of columns under axial impact, Int. J. Solid Struct., 8(7):

5 Aust. J. Basic & Appl. Sci., 5(7): , Karami Korram Abadi M., P. Kazaeinejad and J. Jenabi, 8. "Mecanical Buckling of Functionally graded Beam wit Piezoelectric Actuators", NCME. Tzou, H.S., G.C. Wan, 99. Distributed structural dynamics control of flexible manipulators-i. Structural dynamics and distributed viscoelastic actuator. Computers and Structures, 35(6): Wang C.M., J.N. Reddy,. "Sear Deformable Beams and Plates", Oxford, Elsevier. 747

Journal of Mechanical Science and Technology 23 (2009) 2072~2084. M. M. Najafizadeh * and M. R. Isvandzibaei

Journal of Mechanical Science and Technology 23 (2009) 2072~2084. M. M. Najafizadeh * and M. R. Isvandzibaei Journal of Mecanical Science and Tecnology (9 7~84 Journal of Mecanical Science and Tecnology www.springerlink.com/content/78-494x DOI.7/s6-9-4- Vibration of functionally graded cylindrical sells based

More information

Static Response Analysis of a FGM Timoshenko s Beam Subjected to Uniformly Distributed Loading Condition

Static Response Analysis of a FGM Timoshenko s Beam Subjected to Uniformly Distributed Loading Condition Static Response Analysis of a FGM Timoseno s Beam Subjected to Uniformly Distributed Loading Condition 8 Aas Roy Department of Mecanical Engineering National Institute of Tecnology Durgapur Durgapur, Maatma

More information

6. Non-uniform bending

6. Non-uniform bending . Non-uniform bending Introduction Definition A non-uniform bending is te case were te cross-section is not only bent but also seared. It is known from te statics tat in suc a case, te bending moment in

More information

3. Using your answers to the two previous questions, evaluate the Mratio

3. Using your answers to the two previous questions, evaluate the Mratio MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 0219 2.002 MECHANICS AND MATERIALS II HOMEWORK NO. 4 Distributed: Friday, April 2, 2004 Due: Friday,

More information

Bending analysis of a functionally graded piezoelectric cantilever beam

Bending analysis of a functionally graded piezoelectric cantilever beam Science in Cina Series G: Pysics Mecanics & Astronomy 7 Science in Cina Press Springer-Verlag Bending analysis of a functionally graded pieoelectric cantilever beam YU Tao & ZHONG Zeng Scool of Aerospace

More information

Nonlinear correction to the bending stiffness of a damaged composite beam

Nonlinear correction to the bending stiffness of a damaged composite beam Van Paepegem, W., Decaene, R. and Degrieck, J. (5). Nonlinear correction to te bending stiffness of a damaged composite beam. Nonlinear correction to te bending stiffness of a damaged composite beam W.

More information

WINKLER PLATES BY THE BOUNDARY KNOT METHOD

WINKLER PLATES BY THE BOUNDARY KNOT METHOD WINKLER PLATES BY THE BOUNARY KNOT ETHO Sofía Roble, sroble@fing.edu.uy Berardi Sensale, sensale@fing.edu.uy Facultad de Ingeniería, Julio Herrera y Reissig 565, ontevideo Abstract. Tis paper describes

More information

Euler-Bernoulli Beam Theory in the Presence of Fiber Bending Stiffness

Euler-Bernoulli Beam Theory in the Presence of Fiber Bending Stiffness IOSR Journal of Matematics (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 13, Issue 3 Ver. V (May - June 017), PP 10-17 www.iosrjournals.org Euler-Bernoulli Beam Teory in te Presence of Fiber Bending

More information

Analysis of Stress and Deflection about Steel-Concrete Composite Girders Considering Slippage and Shrink & Creep Under Bending

Analysis of Stress and Deflection about Steel-Concrete Composite Girders Considering Slippage and Shrink & Creep Under Bending Send Orders for Reprints to reprints@bentamscience.ae Te Open Civil Engineering Journal 9 7-7 7 Open Access Analysis of Stress and Deflection about Steel-Concrete Composite Girders Considering Slippage

More information

Thermoelastic Buckling Analysis of Power-law, Sigmoid, Exponential FGM Circular Plates with Piezoelectric Actuators

Thermoelastic Buckling Analysis of Power-law, Sigmoid, Exponential FGM Circular Plates with Piezoelectric Actuators 3rd International Conference on Mecanical, Electronics and Mecatronics Engineering (ICMEME'4) Marc 9-, 4 Abu Dabi (UAE) ermoelastic Buckling Analysis of Power-law, Sigmoid, Exonential FGM Circular Plates

More information

Chapter 2 Buckling and Post-buckling of Beams

Chapter 2 Buckling and Post-buckling of Beams Chapter Buckling and Post-buckling of Beams Abstract This chapter presents buckling and post-buckling analysis of straight beams under thermal and mechanical loads. The Euler and Timoshenko beam theories

More information

AN ANALYSIS OF AMPLITUDE AND PERIOD OF ALTERNATING ICE LOADS ON CONICAL STRUCTURES

AN ANALYSIS OF AMPLITUDE AND PERIOD OF ALTERNATING ICE LOADS ON CONICAL STRUCTURES Ice in te Environment: Proceedings of te 1t IAHR International Symposium on Ice Dunedin, New Zealand, nd t December International Association of Hydraulic Engineering and Researc AN ANALYSIS OF AMPLITUDE

More information

HIGH ORDER SHEAR DEFORMATION THEORY FOR ISOTROPIC BEAMS WITH USING MIXED FINITE ELEMENT METHOD

HIGH ORDER SHEAR DEFORMATION THEORY FOR ISOTROPIC BEAMS WITH USING MIXED FINITE ELEMENT METHOD Held on 1-, Nov, 15, in Dubai, ISBN:978819313731 HIGH ORDER SHEAR DEFORATION THEORY FOR ISOTROPIC BEAS WITH USING IXED FINITE ELEENT ETHOD Emra adenci, Department of Civil Engineering, Necmettin Erbakan

More information

Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties

Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties DR. ŞEREF DOĞUŞCAN AKBAŞ Civil Engineer, Şehit Muhtar Mah. Öğüt Sok. No:2/37, 34435 Beyoğlu- Istanbul,

More information

NCCI: Simple methods for second order effects in portal frames

NCCI: Simple methods for second order effects in portal frames NCC: Simple metods for second order effects in portal frames NCC: Simple metods for second order effects in portal frames NCC: Simple metods for second order effects in portal frames Tis NCC presents information

More information

JOURNAL OF APPLIED SCIENCES RESEARCH

JOURNAL OF APPLIED SCIENCES RESEARCH Copyrigt 15 American-Eurasian Network for Scientific Information publiser JOURNA OF APPIED SCIENCES RESEARCH ISSN: 1819-5X EISSN: 181-157X JOURNA ome page: ttp://www.aensiweb.com/jasr 15 Special; 11(17):

More information

1859. Forced transverse vibration analysis of a Rayleigh double-beam system with a Pasternak middle layer subjected to compressive axial load

1859. Forced transverse vibration analysis of a Rayleigh double-beam system with a Pasternak middle layer subjected to compressive axial load 1859. Forced transverse vibration analysis of a Rayleigh double-beam system with a Pasternak middle layer subjected to compressive axial load Nader Mohammadi 1, Mehrdad Nasirshoaibi 2 Department of Mechanical

More information

A = h w (1) Error Analysis Physics 141

A = h w (1) Error Analysis Physics 141 Introduction In all brances of pysical science and engineering one deals constantly wit numbers wic results more or less directly from experimental observations. Experimental observations always ave inaccuracies.

More information

Flapwise bending vibration analysis of double tapered rotating Euler Bernoulli beam by using the differential transform method

Flapwise bending vibration analysis of double tapered rotating Euler Bernoulli beam by using the differential transform method Meccanica 2006) 41:661 670 DOI 10.1007/s11012-006-9012-z Flapwise bending vibration analysis of double tapered rotating Euler Bernoulli beam by using te differential transform metod Ozge Ozdemir Ozgumus

More information

Unit 18 Other Issues In Buckling/Structural Instability

Unit 18 Other Issues In Buckling/Structural Instability Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your leisure ) Ch. 15, Ch. 16 Theory of Elastic Stability

More information

Critical Load columns buckling critical load

Critical Load columns buckling critical load Buckling of Columns Buckling of Columns Critical Load Some member may be subjected to compressive loadings, and if these members are long enough to cause the member to deflect laterally or sideway. To

More information

Development and experimental verification of a numerical model for optimizing the cleaning performance of the doctor blade press roll tribosystem

Development and experimental verification of a numerical model for optimizing the cleaning performance of the doctor blade press roll tribosystem Development and experimental verification of a numerical model for optimizing te cleaning performance of te doctor blade press roll tribosystem M. Rodríguez Ripoll, B. Sceicl,, D. Bianci, B. Jakab, F.

More information

Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet

Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet Copyright 05 Tech Science Press CMC, vol.8, no., pp.03-7, 05 Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet G. Q. Xie, J. P. Wang, Q. L. Zhang Abstract: Small-scale effect on the

More information

Sample Problems for Exam II

Sample Problems for Exam II Sample Problems for Exam 1. Te saft below as lengt L, Torsional stiffness GJ and torque T is applied at point C, wic is at a distance of 0.6L from te left (point ). Use Castigliano teorem to Calculate

More information

Structural 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 Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

More information

Stress analysis of laminated glass with different interlayer materials

Stress analysis of laminated glass with different interlayer materials Alexandria Engineering Journal (01) 51, 61 67 Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com Stress analysis of laminated glass wit different interlayer

More information

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case

More information

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship Chapter 5 Elastic Strain, Deflection, and Stability Elastic Stress-Strain Relationship A stress in the x-direction causes a strain in the x-direction by σ x also causes a strain in the y-direction & z-direction

More information

Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method

Static 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 information

Dynamic Young s Modulus, Shear and Torsional Moduli of Pine Beams

Dynamic Young s Modulus, Shear and Torsional Moduli of Pine Beams Dynamic Young s Modulus, Sear and Torsional Moduli of Pine Beams In two different teories Seyede Masoume Hasemi Taalvandani Department of Wood and Paper Science and Tecnology, Islamic Azad University,

More information

Bending, Buckling and Vibration of a Functionally Graded Porous Beam Using Finite Elements

Bending, Buckling and Vibration of a Functionally Graded Porous Beam Using Finite Elements J. Appl. Comput. Mec., 3(4) (017) 74-8 DOI: 10.055/JACM.017.194.111 ISSN: 383-4536 jacm.scu.ac.ir Bending, Buckling and Vibration of a Functionally Graded Porous Beam Using Finite Elements Noa Fouda 1,

More information

December 10, PROBLEM NO points max.

December 10, PROBLEM NO points max. PROBLEM NO. 1 25 points max. PROBLEM NO. 2 25 points max. B 3A A C D A H k P L 2L Given: Consider the structure above that is made up of rod segments BC and DH, a spring of stiffness k and rigid connectors

More information

FREE VIBRATION OF AXIALLY LOADED FUNCTIONALLY GRADED SANDWICH BEAMS USING REFINED SHEAR DEFORMATION THEORY

FREE VIBRATION OF AXIALLY LOADED FUNCTIONALLY GRADED SANDWICH BEAMS USING REFINED SHEAR DEFORMATION THEORY FREE VIBRATION OF AXIALLY LOADED FUNCTIONALLY GRADED SANDWICH BEAMS USING REFINED SHEAR DEFORMATION THEORY Thuc P. Vo 1, Adelaja Israel Osofero 1, Marco Corradi 1, Fawad Inam 1 1 Faculty of Engineering

More information

Optimizing the Design of Polymer Based Unimorph Actuator using COMSOL Multiphysics Vineet Tiwari, Rashiya Sharma, R. K. Dwivedi and Geetika Srivastava

Optimizing the Design of Polymer Based Unimorph Actuator using COMSOL Multiphysics Vineet Tiwari, Rashiya Sharma, R. K. Dwivedi and Geetika Srivastava Optimizing the Design of Polymer Based Unimorph Actuator using COMSOL Multiphysics Vineet Tiwari, Rashiya Sharma, R. K. Dwivedi and Geetika Srivastava Department of Physics and Materials Science & Engineering

More information

The New Boundary Condition Effect on The Free Vibration Analysis of Micro-beams Based on The Modified Couple Stress Theory

The New Boundary Condition Effect on The Free Vibration Analysis of Micro-beams Based on The Modified Couple Stress Theory International Research Journal of Applied and Basic Sciences 2015 Available online at www.irjabs.com ISSN 2251-838X / Vol, 9 (3): 274-279 Science Explorer Publications The New Boundary Condition Effect

More information

Lecture 15 Strain and stress in beams

Lecture 15 Strain and stress in beams Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

More information

DEBONDING FAILURES OF RC BEAMS STRENGTHENED WITH EXTERNALLY BONDED FRP REINFORCEMENT: BEHAVIOUR AND MODELLING

DEBONDING FAILURES OF RC BEAMS STRENGTHENED WITH EXTERNALLY BONDED FRP REINFORCEMENT: BEHAVIOUR AND MODELLING Asia-Pacific Conference on FRP in Structures (APFIS 2007) S.T. Smit (ed) 2007 International Institute for FRP in Construction DEBONDING FAILURES OF RC BEAMS STRENGTHENED WITH EXTERNALLY BONDED FRP REINFORCEMENT:

More information

Mechanics of Materials Primer

Mechanics of Materials Primer Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus

More information

NONLINEAR ANALYSIS OF A FUNCTIONALLY GRADED BEAM RESTING ON THE ELASTIC NONLINEAR FOUNDATION

NONLINEAR ANALYSIS OF A FUNCTIONALLY GRADED BEAM RESTING ON THE ELASTIC NONLINEAR FOUNDATION Journal of Theoretical and Applied Mechanics, Sofia, 2014, vol. 44, No. 2, pp. 71 82 NONLINEAR ANALYSIS OF A FUNCTIONALLY GRADED BEAM RESTING ON THE ELASTIC NONLINEAR FOUNDATION M. Arefi Department of

More information

232 Calculus and Structures

232 Calculus and Structures 3 Calculus and Structures CHAPTER 17 JUSTIFICATION OF THE AREA AND SLOPE METHODS FOR EVALUATING BEAMS Calculus and Structures 33 Copyrigt Capter 17 JUSTIFICATION OF THE AREA AND SLOPE METHODS 17.1 THE

More information

Vibration in a Cracked Machine Tool Spindle with Magnetic Bearings

Vibration in a Cracked Machine Tool Spindle with Magnetic Bearings Te Open Mecanical Engineering Journal, 8,, 3-39 3 Open Access Vibration in a Cracked Macine Tool Spindle wit Magnetic Bearings Huang-Kuang Kung and Bo-Wun Huang Department of Mecanical Engineering, Ceng

More information

MODIFIED 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 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 * E-Mail: jasos91@hotmail.com,

More information

Torsional Buckling of Double-Walled Carbon Nanotubes

Torsional Buckling of Double-Walled Carbon Nanotubes Torsional Buckling of Double-Walled Carbon Nanotubes S. H. Soong Engineering Science Programme, National University of Singapore Kent Ridge, Singapore 119260 ABSTRACT This paper is concerned with the torsional

More information

Path to static failure of machine components

Path to static failure of machine components Pat to static failure of macine components Load Stress Discussed last week (w) Ductile material Yield Strain Brittle material Fracture Fracture Dr. P. Buyung Kosasi,Spring 008 Name some of ductile and

More information

EFFECTS OF LINE AND PASSIVATION GEOMETRY ON CURVATURE EVOLUTION DURING PROCESSING AND THERMAL CYCLING IN COPPER INTERCONNECT LINES

EFFECTS OF LINE AND PASSIVATION GEOMETRY ON CURVATURE EVOLUTION DURING PROCESSING AND THERMAL CYCLING IN COPPER INTERCONNECT LINES Acta mater. 48 (000) 3169±3175 www.elsevier.com/locate/actamat EFFECTS OF LINE AND PASSIVATION GEOMETRY ON CURVATURE EVOLUTION DURING PROCESSING AND THERMAL CYCLING IN COPPER INTERCONNECT LINES T.-S. PARK

More information

Simulation of functionally graded material beam with Piezoelectric Actuators

Simulation of functionally graded material beam with Piezoelectric Actuators Simulation of functionally graded material beam with Piezoelectric Actuators Bendine Kouider 1,Satla Zouaoui 1, Boukhoulda Farouk Benallal 1, el ajrami Mohammed 1 1 Structures and Solid Mechanical Laboratory,

More information

CHAPTER 5. Beam Theory

CHAPTER 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 Euler-Bernoulli assumptions One of its dimensions

More information

Stability of Functionally Graded Plate under In-Plane Time-Dependent Compression

Stability of Functionally Graded Plate under In-Plane Time-Dependent Compression Mechanics and Mechanical Engineering Vol. 7, No. 2 (2004) 5 12 c Technical University of Lodz Stability of Functionally Graded Plate under In-Plane Time-Dependent Compression Andrzej TYLIKOWSKI Warsaw

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY O SASKATCHEWAN Department of Pysics and Engineering Pysics Pysics 117.3 MIDTERM EXAM Regular Sitting NAME: (Last) Please Print (Given) Time: 90 minutes STUDENT NO.: LECTURE SECTION (please ceck):

More information

COMPARATIVE THERMAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATE

COMPARATIVE THERMAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATE HERMAL SCIENCE: Year 7, Vol., No. 6B, pp. 957-969 957 Introduction COMPARAIVE HERMAL BUCKLING ANALYSIS OF FUNCIONALLY GRADED PLAE by Dragan V. ČUKANOVIĆ a*, Gordana M. BOGDANOVIĆ b, Aleksandar B. RADAKOVIĆ

More information

Physics 121, April 1, Equilibrium. Physics 121. April 1, Physics 121. April 1, Course Information. Discussion of Exam # 2

Physics 121, April 1, Equilibrium. Physics 121. April 1, Physics 121. April 1, Course Information. Discussion of Exam # 2 Pysics 121, April 1, 2008. Pysics 121. April 1, 2008. Course Information Discussion of Exam # 2 Topics to be discussed today: Requirements for Equilibrium Gravitational Equilibrium Sample problems Pysics

More information

Advances in Materials Science and Applications 2016, Vol. 5 Iss. 1, PP. 1-11

Advances in Materials Science and Applications 2016, Vol. 5 Iss. 1, PP. 1-11 Advances in Materials Science and Applications 6 Vol. 5 Iss. PP. - First online: 4 April 6 Dynamic Analysis of Simply Supported Functionally Graded Nanobeams Subjected to a Moving Force Based on the Nonlocal

More information

PECULIARITIES OF THE WAVE FIELD LOCALIZATION IN THE FUNCTIONALLY GRADED LAYER

PECULIARITIES OF THE WAVE FIELD LOCALIZATION IN THE FUNCTIONALLY GRADED LAYER Materials Pysics and Mecanics (5) 5- Received: Marc 7, 5 PECULIARITIES OF THE WAVE FIELD LOCALIZATION IN THE FUNCTIONALLY GRADED LAYER Т.I. Belyankova *, V.V. Kalincuk Soutern Scientific Center of Russian

More information

THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH CYLINDERS OF FUNCTIONALLY GRADED MATERIALS

THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH CYLINDERS OF FUNCTIONALLY GRADED MATERIALS Journal of Thermal Stresses, 28: 391 408, 2005 Copyright # Taylor & Francis Inc. ISSN: 0149-5739 print/1521-074x online DOI: 10.1080/01495730590916623 THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH

More information

ANALYTICAL INVESTIGATION OF NONLINEAR MODEL ARISING IN HEAT TRANSFER THROUGH THE POROUS FIN

ANALYTICAL INVESTIGATION OF NONLINEAR MODEL ARISING IN HEAT TRANSFER THROUGH THE POROUS FIN ANALYTICAL INVESTIGATION OF NONLINEAR MODEL ARISING IN HEAT TRANSFER THROUGH THE POROUS FIN Yasser ROSTAMIYAN a, Davood Domiri GANJI a*, Iman RAHIMI PETROUDI b, and Medi KHAZAYI NEJAD a a Department of

More information

Bending Analysis of a Cantilever Nanobeam With End Forces by Laplace Transform

Bending Analysis of a Cantilever Nanobeam With End Forces by Laplace Transform International Journal of Engineering & Applied Sciences (IJEAS) Vol.9, Issue (Special Issue: Composite Structures) (07) 03- http://.doi.org/0.407/ijeas.34635 Int J Eng Appl Sci 9() (07) 03- Bending Analysis

More information

needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns.

needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns. CHAPTER OBJECTIVES Discuss the behavior of columns. Discuss the buckling of columns. Determine the axial load needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods

More information

Numerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams

Numerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams Numerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams Fatemeh Farhatnia, Gholam-Ali Sharifi and Saeid Rasouli Abstract In this paper, thermo-mechanical stress distribution has been

More information

ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM BEHAVIOR UNDER THE EFFECT OF EXTERNAL SOLICITATIONS

ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM BEHAVIOR UNDER THE EFFECT OF EXTERNAL SOLICITATIONS Third International Conference on Energy, Materials, Applied Energetics and Pollution. ICEMAEP016, October 30-31, 016, Constantine,Algeria. ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM

More information

Vibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai Huang1, *

Vibro-acoustic 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) Vibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai

More information

NUMERICAL EVALUATION OF A TEFLON BASED PIEZOELECTRIC SENSOR EFFECTIVITY FOR THE MONITORING OF EARLY AGE COCRETE STRENGTHING

NUMERICAL EVALUATION OF A TEFLON BASED PIEZOELECTRIC SENSOR EFFECTIVITY FOR THE MONITORING OF EARLY AGE COCRETE STRENGTHING NUMERICAL EVALUATION OF A TEFLON BASED PIEZOELECTRIC SENSOR EFFECTIVITY FOR THE MONITORING OF EARLY AGE COCRETE STRENGTHING Evangelos V. Liarakos Postdoctoral researcher School of Architecture, Technical

More information

AMS 147 Computational Methods and Applications Lecture 09 Copyright by Hongyun Wang, UCSC. Exact value. Effect of round-off error.

AMS 147 Computational Methods and Applications Lecture 09 Copyright by Hongyun Wang, UCSC. Exact value. Effect of round-off error. Lecture 09 Copyrigt by Hongyun Wang, UCSC Recap: Te total error in numerical differentiation fl( f ( x + fl( f ( x E T ( = f ( x Numerical result from a computer Exact value = e + f x+ Discretization error

More information

CALCULATION OF COLLAPSE PRESSURE IN SHALE GAS FORMATION AND THE INFLUENCE OF FORMATION ANISOTROPY

CALCULATION OF COLLAPSE PRESSURE IN SHALE GAS FORMATION AND THE INFLUENCE OF FORMATION ANISOTROPY CALCULATION OF COLLAPSE PRESSURE IN SHALE GAS FORMATION AND THE INFLUENCE OF FORMATION ANISOTROPY L.Hu, J.Deng, F.Deng, H.Lin, C.Yan, Y.Li, H.Liu, W.Cao (Cina University of Petroleum) Sale gas formations

More information

Recent Advances on Mechanics, Materials, Mechanical Engineering and Chemical Engineering

Recent Advances on Mechanics, Materials, Mechanical Engineering and Chemical Engineering Size-dependent pull-in analysis of electrically actuated micro-plates based on the modified couple stress theory Arman Mohsenzadeh,a, Masoud Tahani,b*, Amir Reza Askari,c,, Department of Mechanical Engineering,

More information

Chapters 19 & 20 Heat and the First Law of Thermodynamics

Chapters 19 & 20 Heat and the First Law of Thermodynamics Capters 19 & 20 Heat and te First Law of Termodynamics Te Zerot Law of Termodynamics Te First Law of Termodynamics Termal Processes Te Second Law of Termodynamics Heat Engines and te Carnot Cycle Refrigerators,

More information

FINAL EXAMINATION. (CE130-2 Mechanics of Materials)

FINAL EXAMINATION. (CE130-2 Mechanics of Materials) UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. GTE 2016 Q. 1 Q. 9 carry one mark each. D : SOLID MECHNICS Q.1 single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system

More information

Large deflection analysis of rhombic sandwich plates placed on elastic foundation

Large deflection analysis of rhombic sandwich plates placed on elastic foundation Indian Journal of Engineering & Materials Sciences Vol. 5, February 008, pp. 7-3 Large deflection analysis of rombic sandic plates placed on elastic foundation Gora Cand Cell a*, Subrata Mondal b & Goutam

More information

March 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE

March 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano

More information

ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING

ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING PURPOSE 01 January 2000 / mgj The purpose of this exercise is to study the effects of end conditions, column length, and material properties

More information

Buckling of Laminated and Functionally Graded Plates using Radial Basis Functions

Buckling of Laminated and Functionally Graded Plates using Radial Basis Functions Paper 223 Buckling of Laminated and Functionally Graded Plates using Radial Basis Functions A.M.A. Neves, A.J.M. Ferreira, E. Carrera 3, M. Cinefra 3 C.M.C. Roque 2, C.M. Mota Soares 4 and R.M.N. Jorge

More information

HT TURBULENT NATURAL CONVECTION IN A DIFFERENTIALLY HEATED VERTICAL CHANNEL. Proceedings of 2008 ASME Summer Heat Transfer Conference HT2008

HT TURBULENT NATURAL CONVECTION IN A DIFFERENTIALLY HEATED VERTICAL CHANNEL. Proceedings of 2008 ASME Summer Heat Transfer Conference HT2008 Proceedings of 2008 ASME Summer Heat Transfer Conference HT2008 August 10-14, 2008, Jacksonville, Florida USA Proceedings of HT2008 2008 ASME Summer Heat Transfer Conference August 10-14, 2008, Jacksonville,

More information

Stress analysis of a stepped bar

Stress analysis of a stepped bar Stress analysis of a stepped bar Problem Find the stresses induced in the axially loaded stepped bar shown in Figure. The bar has cross-sectional areas of A ) and A ) over the lengths l ) and l ), respectively.

More information

Optimization of the thin-walled rod with an open profile

Optimization of the thin-walled rod with an open profile (1) DOI: 1.151/ matecconf/181 IPICSE-1 Optimization of te tin-walled rod wit an open profile Vladimir Andreev 1,* Elena Barmenkova 1, 1 Moccow State University of Civil Engineering, Yaroslavskoye s., Moscow

More information

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012 Lecture Slides Chapter 4 Deflection and Stiffness The McGraw-Hill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration

More information

Nonlinear Bending and Thermal Post-Buckling Analysis of FGM Beams Resting on Nonlinear Elastic Foundations

Nonlinear Bending and Thermal Post-Buckling Analysis of FGM Beams Resting on Nonlinear Elastic Foundations Copyright 014 Tech Science Press CMES, vol.100, no.3, pp.01-, 014 Nonlinear Bending and Thermal Post-Buckling Analysis of FGM Beams Resting on Nonlinear Elastic Foundations Da-Guang Zhang 1, and Hao-Miao

More information

Nonlinear 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 Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory Tai-Ping Chang 1 and Quey-Jen Yeh 1 Department of Construction Engineering, National Kaohsiung First

More information

Comb resonator design (2)

Comb resonator design (2) Lecture 6: Comb resonator design () -Intro Intro. to Mechanics of Materials School of Electrical l Engineering i and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory

More information

Large eddy simulation of turbulent flow downstream of a backward-facing step

Large eddy simulation of turbulent flow downstream of a backward-facing step Available online at www.sciencedirect.com Procedia Engineering 31 (01) 16 International Conference on Advances in Computational Modeling and Simulation Large eddy simulation of turbulent flow downstream

More information

Model development for the beveling of quartz crystal blanks

Model development for the beveling of quartz crystal blanks 9t International Congress on Modelling and Simulation, Pert, Australia, 6 December 0 ttp://mssanz.org.au/modsim0 Model development for te beveling of quartz crystal blanks C. Dong a a Department of Mecanical

More information

COLUMNS: BUCKLING (DIFFERENT ENDS)

COLUMNS: BUCKLING (DIFFERENT ENDS) COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pin-connected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43

More information

Thermal buckling and post-buckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method

Thermal buckling and post-buckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method hermal buckling and post-buckling 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 information

Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6.2, 6.3

Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6.2, 6.3 M9 Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6., 6.3 A shaft is a structural member which is long and slender and subject to a torque (moment) acting about its long axis. We

More information

Simulation and verification of a plate heat exchanger with a built-in tap water accumulator

Simulation and verification of a plate heat exchanger with a built-in tap water accumulator Simulation and verification of a plate eat excanger wit a built-in tap water accumulator Anders Eriksson Abstract In order to test and verify a compact brazed eat excanger (CBE wit a built-in accumulation

More information

Section A 01. (12 M) (s 2 s 3 ) = 313 s 2 = s 1, h 3 = h 4 (s 1 s 3 ) = kj/kgk. = kj/kgk. 313 (s 3 s 4f ) = ln

Section A 01. (12 M) (s 2 s 3 ) = 313 s 2 = s 1, h 3 = h 4 (s 1 s 3 ) = kj/kgk. = kj/kgk. 313 (s 3 s 4f ) = ln 0. (a) Sol: Section A A refrigerator macine uses R- as te working fluid. Te temperature of R- in te evaporator coil is 5C, and te gas leaves te compressor as dry saturated at a temperature of 40C. Te mean

More information

Basic Energy Principles in Stiffness Analysis

Basic Energy Principles in Stiffness Analysis Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting

More information

Free Vibration Analysis of Functionally Graded Material Plates with Various Types of Cutouts using Finite Element Method

Free Vibration Analysis of Functionally Graded Material Plates with Various Types of Cutouts using Finite Element Method International Journal of Current Engineering and Technology E-ISSN 2277 4106, P-ISSN 2347 5161 2018 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Free

More information

Finite Element Analysis of Piezoelectric Cantilever

Finite 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 information

BUCKLING OF VARIABLE CROSS-SECTIONS COLUMNS IN THE BRACED AND SWAY PLANE FRAMES

BUCKLING OF VARIABLE CROSS-SECTIONS COLUMNS IN THE BRACED AND SWAY PLANE FRAMES ROCZNIKI INŻYNIERII BUDOWLANEJ ZESZYT 16/016 Komisja Inżynierii Budowlanej Oddział Polskiej Akademii Nauk w Katowicach BUCKLING OF VARIABLE CROSS-SECTIONS COLUMNS IN THE BRACED AND SWAY PLANE FRAMES Ružica

More information

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department

More information

A general articulation angle stability model for non-slewing articulated mobile cranes on slopes *

A general articulation angle stability model for non-slewing articulated mobile cranes on slopes * tecnical note 3 general articulation angle stability model for non-slewing articulated mobile cranes on slopes * J Wu, L uzzomi and M Hodkiewicz Scool of Mecanical and Cemical Engineering, University of

More information

INTRODUCTION TO STRAIN

INTRODUCTION TO STRAIN SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,

More information

Unit 13 Review of Simple Beam Theory

Unit 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 10-15 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics

More information

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,

More information

Mechanical Design in Optical Engineering

Mechanical Design in Optical Engineering OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:

More information

Application of piezoelectric actuators to active control of composite spherical caps

Application of piezoelectric actuators to active control of composite spherical caps Smart Mater. Struct. 8 (1999 18. Printed in the UK PII: S964-176(991661-4 Application of piezoelectric actuators to active control of composite spherical caps Victor Birman, Gareth J Knowles and John J

More information

Fabric Evolution and Its Effect on Strain Localization in Sand

Fabric Evolution and Its Effect on Strain Localization in Sand Fabric Evolution and Its Effect on Strain Localization in Sand Ziwei Gao and Jidong Zao Abstract Fabric anisotropy affects importantly te overall beaviour of sand including its strengt and deformation

More information

Temperature Dependent and Independent Material Properties of FGM Plates

Temperature 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 information

Chapter 4 Deflection and Stiffness

Chapter 4 Deflection and Stiffness Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 4-1 Spring Rates 4-2 Tension, Compression, and Torsion 4-3 Deflection Due to Bending 4-4 Beam

More information

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

More information