Engineering Analysis With Maple/Mathematica
The variational, finite element, and finite difference methods constitute the very core of engineering analysis, but the associated computations are tedious at best, and often obscure both the ideas and the techniques of the approach. This book shows how using symbolic codes to provide analytical results in engineering design makes the process easier, and allows students to concentrate on the underlying ideas of engineering analysis, rather than being hampered by its associated calculations. The text is divided into five parts, covering topics ranging from basic information on symbolic codes through solving engineering problems with them. A disk is included written for Maple and Mathematica(r), to enable the reader to experiment freely with a variety of problems. Key Features * Presents symbolic computation codes which allows students to focus on ideas rather than on calculation difficulties when performing engineering analysis * Introduces the basic concepts of the variational approach and direct techniques * Outlines the finite element method * Analyzes the finite difference approach, considering both the ordinary and partial differential equations * Contains a chapter comprised of practical problems with solutions * Includes a disk written for Maple/Mathematica (r), which allows the user to experiment with a variety of problems
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M2 Repetitions conditionals expansions and integrations
M7 Tables and matrices
6 other sections not shown
accuracy algorithm applies assembly stiffness matrix assume beam element boundary conditions Bubnov-Galerkin method clamped coefficients Consider constant constraint convenient convergence deflection degrees of freedom denoted derivatives diff difference scheme differential equations direct methods displacement vector domain elastic equilibrium equations Euler Euler-Lagrange equation evalf exact solution example expanded matrices explicit expression field variable finite difference finite element method formulate given governing equation Hamilton's principle heat conduction implicit scheme initial conditions integration interpolation iterations Lagrange multipliers linear MAPLE file MAPLEfile MATHEMATICA nodal forces nodal quantities nodes notation Note number of degrees odod operator plate polynomial potential energy prettyprint problem procedure Rayleigh-Ritz method relation relevant respectively Runge-Kutta method shape functions shown in Fig simultaneous equations solve specify stationarity step-size stiffness matrix strain energy subs substitute symbolic computation system of equations technique temperature term trial functions unknown values vanish variation yields