Simulation Based Engineering in Solid Mechanics

by J.S. Rao

Preface.- Introduction.- 1.1 Matrices.- 1.2 Vectors and Tensors.- 1.3 Energy Principle.- 2 Continuous Solid.- 2.1 External and Internal Tractions.- 2.2. Stress Definition.- 2.3. Equilibrium Relations.- 2.4. Strain.- 2.5. Stress -- Strain Relations.- 2.6 Strain Energy and Work.- 2.7 Von Mises Stress.- 3 Euler-Lagrange Equations.- 3.1 General Approach for solving Structural Problems.- 3.2 Other Applications of Euler-Lagrange Equation leading to Optimization.- 3.3 Derivation of Euler-Lagrange Equation through Delta Operator.- 4 Axially Loaded 1-D Structures.- 4.1 Simply Supported Bar.- 4.2 Simply Supported - Free Bar.- 4.3 Finite Element Method.- 4.4 Thermal Stresses.- 4.5 Principle of Virtual Work.- 4.6 Minimization of Total Potential Energy.- 5 Twisting of a Rod.- 5.1 Finite Element Method for Torsion.- 5.2 Two Elements and Stiffness Matrix Assembly.- 5.3 Ritz Method for Torsion.- 6 Bending of a Beam.- 6.1 Bending by Energy Method.- 6.2 Beam with Axial Load (Beam-Column).- 6.3 Strength of Materials Approach.- 6.4 Beam Solution by Energy Method.- 6.5 Beam Finite Element.- 6.6 Buckling revisited.- 6.7 Galerkin Method for Tapered Beams.- 6.8 General Structures by Commercial Solvers.- 7. Epilogue.- Acknowledgements.- Index.

216 pages, Paperback

Published November 9, 2016