# Energy and Finite Element Methods in Structural Mechanics

New Age International, 1995 - Calculus of variations - 757 pages
This Book Is The Outcome Of Material Used In Senior And Graduate Courses For Students In Civil, Mechanical And Aeronautical Engineering. To Meet The Needs Of This Varied Audience, The Author Have Laboured To Make This Text As Flexible As Possible To Use.Consequently, The Book Is Divided Into Three Distinct Parts Of Approximately Equal Size. Part I Is Entitled Foundations Of Solid Mechanics And Variational Methods, Part Ii Is Entitled Structural Mechanics; And Part Iii Is Entitled Finite Elements.Depending On The Background Of The Students And The Aims Of The Course Selected Portions Can Be Used From Some Or All Of The Three Parts Of The Text To Form The Basis Of An Individual Course.The Purpose Of This Useful Book Is To Afford The Student A Sound Foundation In Variational Calculus And Energy Methods Before Delving Into Finite Elements. He Goal Is To Make Finite Elements More Understandable In Terms Of Fundamentals And Also To Provide The Student With The Background Needed To Extrapolate The Finite Element Method To Areas Of Study Other Than Solid Mechanics. In Addition, A Number Of Approximation Techniques Are Made Available Using The Quadratic Functional For A Boundary-Value Problem.Finally, The Authors; Aim Is To Give Students Who Go Through The Entire Text A Balanced And Connected Exposure To Certain Key Aspects Of Modern Structural And Solid Mechanics.

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### Contents

 FOUNDATIONS OF SOLID MECHANICS 1 Equations of Motion 9 Strain 20 The Rotation Tensor 29 General Considerations 37 Hookes Law 43 INTRODUCTION TO THE CALCULUS OF VARIATIONS 66 VARIATIONAL PRINCIPLES OF ELASTICITY 111
 ill FINITE ELEMENTS 455 More General Preliminary Considerations 474 FINITE ELEMENTS FOR BEAMS 487 ELEMENTS AND INTERPOLATION FUNCTIONS 510 indicates that section is in fine print 514 ThreeDimensional Elements 530 PLANE STRESS 543 FINITE ELEMENTS FOR PLATES 574

 Tlic Castigliano Tlicorems and Structural Mechanics 139 Approximate Methods 167 II 183 TORSION 229 CLASSICAL THEORY OF PLATES 257 DYNAMICS OF BEAMS AND PLATES 323 Plates 351 General Considerations 375 of the RayleighRitz Method 386 ELASTIC STABILITY 392 Elastic Stability of Columns 410 Elastic Stability of Plates 429 15IS The Rectangular Plate via the Energy Method 436
 Rectangular Elements 596 Hermite Polynomial Elements 606 Results for Uniformly Loaded Clamped Plate 612 FINITE ELEMENTS FOR ELASTIC STABILITY 628 FINITE ELEMENTS FOR DYNAMICS 643 BROADER ASPECTS OF FINITE ELEMENTS 659 SteadyState Heat Conduction 674 Method of Weighted Residuals Galerkin s Method 688 APPENDICES 709 To Show that Lagrange Multipliers Are Zero for Development 728 Plate Program for Triangular and Rectangular Elements Fortran IV 739 Author Index 749 Copyright