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Analytical solutions of plane structures using Mathematica

Rafael Picon
Organization: Industrial Engineering School
Department: Department of Continuum Mechanics
Journal / Anthology

International Journal for Numerical Methods in Engineering
Year: 2001
Volume: 50
Page range: 969-992

A study investigating the possibilities of using the program Mathematica to obtain analytical solutions of plane structures is presented. Two typical applications are developed: plane frames with only bending deformations and plane trusses. In an attempt to keep the number of unknowns as low as possible, the indirect stiffness method and the force method are used to state the first and the second problems, respectively. All the formulations are developed by making use of kernel and generalized inverse matrices, which are also used to characterize the solution of overd termined systems of equations. Two programs (PlaneFrame and PlaneTruss) were written to solve the first and second problems and the listing of the codes are given in the paper. The results obtained show that problems of a certain complexity can be solved.

*Science > Physics > Mechanics

plane structures, analytical solutions, sti ness method, force method, Mathematica