A.I. Beltzer
Academic Press, 1995
ISBN 0-12-085570-4
Contents
introduction to maple and mathematica
symbolic manipulation codes --- first sessions with maple --- repetitions, conditionals, expansions and integrations --- arrays and matrices --- solving equations --- hints --- first sessions with mathematica --- tables and matrices --- solving equations --- hints.
direct variational methods
direct methods --- functional and its stationarity --- hamilton's principle --- minimum of potential energy --- the bubnov-galerkin method --- beam on elastic foundation --- the rayleigh-ritz method --- master program --- applications --- considerations of accuracy --- mathematical considerations --- operators --- energy convergence and minimum theorem --- more on trial functions --- methods of weighted residual --- the iterative kantorovich method --- heat transfer in a plate --- constraints --- computer-generated euler-lagrange equations --- two degrees of freedom --- continuous systems --- automatic derivation of governing equations --- nature of extremum --- transversality conditions --- generalizations --- gauss' principle --- minimum pressure drag --- approximating boundary conditions --- use of logical expressions --- concluding remarks.
finite element methods
finite element --- stiffness matrix and shape functions --- energy analysis --- truss element --- physical meaning of the matrices --- eigenvalues of stiffness matrix --- reference systems --- generalizations --- assembling --- assembling via equilibrium equations --- assembling via connectivity --- applications to a truss --- inhomogeneous beam --- applications to a beam --- automatic generation of an assembly matrix --- optimization --- imposition of constraints --- free vibrations --- plate element --- programing for plate element --- applications --- two-dimensional elasticity, 1 --- two-dimensional elasticity, 2 --- heat conduction and related problems --- the bubnov-galerkin formulation --- heat transfer in a fin --- numerical example --- time-hystory analysis --- numerical example --- natural reference systems --- serendipity coordinates --- concept of isoparametric elements --- three-node isoparametric bar element --- two-dimensional isoparametric element --- programming for an isoparametric element --- special elements --- constraints and lagrange multipliers --- constraints and penalty parameters --- accuracy, convergence and related subjects --- more on element deficiency --- symbolic database --- concluding remarks.
finite-difference methods
finite differences --- fd - operators and their accuracy --- further about accuracy --- sample problem --- runge-kutta methods, 1 --- runge-kutta methods, 2 --- transient vibrations --- multi-step schemes --- automatic generation of multi-step schemes --- start-up for multi-step schemes --- predictor - corrector methods --- non-linear vibrations --- newmark's method --- finite difference equations --- stability --- solving non-linear equations --- boundary-value problems --- discretization of pde-s --- explicit scheme --- implicit scheme --- stability --- consistency --- other fd-schemesm --- treatment of boundary conditions --- heat conduction (explicit scheme) --- heat conduction (implicit scheme) --- heat conduction in a solidifying alloy, 1 --- heat conduction in a solidifying alloy, 2 --- treatment of irregular boundaries --- torsion of a shaft, 1 --- torsion of a shaft, 2 --- concluding remarks.
workshop
analysis of plates, 1 ---
analysis of plates, 2 ---
analysis of a shock-absorber, 1 ---
analysis of a shock-absorber, 2 ---
flow through a duct ---
free vibrations by the rayleigh-ritz method ---
applications, 1 ---
applications, 2 ---
free vibrations by the bubnov-galerkin method ---
nonlinear free vibrations ---
applications of gauss' principle ---
heat transfer to fluid ---
problems ---
appendix ---
programs (disk included) ---
references.