Energy and Finite Element Methods in Structural Mechanics

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New Age International, 1995 - Calculus of variations - 757 pages
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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
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