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FEM Programs for Plane Trusses and Frames



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22 FEM Programs for Plane Trusses and Frames 22 1 Chapter 22 FEM PROGRAMS FOR PLANE TRUSSES AND FRAMES 22 2 TABLE OF CONTENTS Page 22 1 Introduction 22 2 Analysis Stages 22 3 Analysis Support Modules 22 3 1 Assembling the Master Stiffness 22 3 2 Modifying the Master Stiffness Equations 22 3 3 Internal Force Recovery 22 3 4 Graphic Modules 22 4 A Bridge Truss Example 22 Exercises 22 2 22 3 22 3 22 3 22 3 22 5 22 6 22 6 22 6 22 11 22 3 22 3 ANALYSIS SUPPORT MODULES 22 1 Introduction This Chapter presents a complete FEM program for analysis of plane trusses programmed in Mathematica The program includes some simple minded graphics including animation Exercises 22 2 22 4 discuss a complete FEM program for frame analysis for homework assignments The description is done in bottom up fashion That means the basic modules are presented then the driver program Graphic modules are provided in posted Notebooks but not explained 22 2 Analysis Stages As in all FEM programs the analysis of a structure by the Direct Stiffness Method involves three major stages I preprocessing or model definition II processing and III postprocessing The preprocessing portion of the plane truss analysis is done by the driver program which directly sets the data structures I 1 Model definition by direct setting of the data structures I 2 Plot of the FEM mesh including nodes and element labels The processing stage involves three steps II 1 Assembly of the master stiffness matrix with a subordinate element stiffness module II 2 Modification of master stiffness matrix and node force vector for displacement boundary conditions II 3 Solution of the modified equations for displacements For the programs presented here the built in Mathematica function LinearSolve is used Upon executing these three processing steps the displacements are available The following postprocessing steps may follow III 1 Recovery of forces including reactions done through a Ku matrix multiplication III 2 Computation of internal



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