Analytical solutions of plane structures using Mathematica

摘要

A study in 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 overdetermined 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.