Fundamentals of Structural MechanicsThe last few decades have witnessed a dramatic increase in the application of numerical computation to problems in solid and structural mechanics. The burgeoning of computational mechanics opened a pedagogical gap between traditional courses in elementary strength of materials and the finite element method that classical courses on advanced strength of materials and elasticity do not adequately fill. In the past, our ability to formulate theory exceeded our ability to compute. In those days, solid mechanics was for virtuosos. With the advent of the finite element method, our ability to compute has surpassed our ability to formulate theory. As a result, continuum mechanics is no longer the province of the specialist. What an engineer needs to know about mechanics has been forever changed by our capacity to compute. This book attempts to capitalize on the pedagogi cal opportunities implicit in this shift of perspective. It now seems more ap propriate to focus on fundamental principles and formulations than on classical solution techniques. |
Contents
The Geometry of Deformation | 57 |
Elastic Constitutive Theory | 131 |
Boundary Value Problems in Elasticity 159 | 158 |
The Ritz Method of Approximation | 193 |
The Linear Theory of Beams | 241 |
The Linear Theory of Plates 293 | 292 |
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Common terms and phrases
approximation axial axis base functions base vectors basis beam theory bifurcation diagram body force boundary conditions boundary value problem buckling coefficients components compute Consider constant constitutive equations critical load cross section curve defined deformation map deformed configuration differential equations directional derivative displacement field divergence divergence theorem dot product e₁ e₂ eigenvalues eigenvectors elastic energy functional equilibrium equations equilibrium path example expression external virtual Figure Find finite element given integral length linear matrix mechanics modulus motion Newton's method nonlinear normal vector notation orthogonal parameter plane plate polynomial principle of virtual rate of change Ritz method rotation satisfy scalar field second derivative shear shown in Fig simply solution solve stability strain tensor stress tensor stretch summation surface tangent tensor field theorem three-dimensional tion traction vector transverse undeformed unit vector field virtual displacement virtual-work functional volume zero