Applied Finite Element Analysis
This book is intended for presenting the basic concepts of Finite Element Analysis applied to several engineering applications. Salient Features: 1. Covers several modules of elasticity, heat conduction, eigenvalue and fluid flow analysis which are necessary for a student of Mechanical Engineering. 2. Finite Element formulations have been presented using both global and natural coordinates. It is important for providing smooth transition form formulation in global coordinates to natural coordinates. 3. Special focus has been given to heat conduction problems and fluid flows which are not sufficiently discussed in other textbooks. 4. Important factors affecting the formulation have been included as Miscellaneous Topics. 5. Several examples have been worked out in order to highlight the applications of Finite Element Analysis. New to this Edition Apart from moderately revising the whole text three new chapters "Dynamic Analysis", "Non-linear Analysis", "Bending of Thin Plates", three appendices and short questions and answers have been added in the present edition to make it more useful.
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beam element body force boundary conditions calculated convection deflection degrees of freedom differential equation Discretisation displacement vector eigenvalue eigenvector elasticity element equations element load vector Element matrices element shown element stiffness matrix essential boundary conditions evaluated expressed field variable FIGURE Finite Element Analysis finite element method force vector geometric global coordinate global coordinate system Global load vector global stiffness matrix heat flux Hence integral inverse iteration iteration mass matrix material property matrix mode shape natural coordinate Nodal coordinates nodal degrees nodal displacement vector nodal temperatures non-linear number of elements number of nodes obtained One-dimensional linear element plane strain plane stress plate polynomial potential energy problem Rayleigh Quotient shape functions shown in Fig solution solving stepped bar Strain-displacement matrix symmetric symmetric matrix system equations Thermal triangular element two-dimensional variation