Variational Principles of Theory of Elasticity with Applications |
Contents
Foreword | 1 |
1 | 10 |
13 | 28 |
Beam Theory With Two Generalized Displace | 127 |
Bending of Thin Plates | 184 |
conditions | 222 |
Natural Vibrations and Stability of Thin Plates | 264 |
midplane forces | 278 |
ThreeDimensional Problems of Theory | 299 |
Plane Problems of Elasticity | 357 |
Bending Theory of Plates with Three Generalized | 381 |
Shallow Shells | 425 |
| 474 | |
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Common terms and phrases
a²w admissible argument functions beam boundary conditions C₁ classical theory compatible corresponding critical load curvature deflection denotes derivatives differential equation displacement boundary conditions dx dx dxdy eigenfunctions eigenvalue problem energy density equations of equilibrium evaluated exact solution Əx² Əy² finite element method flexural rigidity follows Gaussian curvature Hence integral internal forces interpolation formula Lagrange multiplier linear M₂ membrane theory midsurface minimum complementary energy minimum potential energy natural frequencies node obtains P₁ plane stress plate bending polynomial principle of minimum Ritz method satisfy shallow shells shearing force shown in Fig simply supported static problem statically determinate stiffness matrix strain energy strain energy density stress function Substituting theorem two-field variational expression variational principle vibration problems w₁ w₂ θω әм ди дп ду дх ду дхду მდ მს