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## FINITE ELEM METHODS

by: Mason Hackett

81

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1

# FINITE ELEM METHODS CEE 504

Mason Hackett
UW
GPA 3.91

Staff

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COURSE
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PAGES
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KARMA
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## Popular in Civil and Environmental Engineering

This 1 page Study Guide was uploaded by Mason Hackett on Wednesday September 9, 2015. The Study Guide belongs to CEE 504 at University of Washington taught by Staff in Fall. Since its upload, it has received 81 views. For similar materials see /class/191986/cee-504-university-of-washington in Civil and Environmental Engineering at University of Washington.

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Date Created: 09/09/15
CEE 504 Finite Element Methods in Structural Mechanics Midterm Exam Study Questions 1 February 2007 The Theory of the Finite Element Method 1 How do we know what continuity and completeness requirements the displacement field that we use in our finite element formulation must satisfy 2 Given continuity and completeness requirements how do you know if your shape functions satisfy them 3 Why do we use the PMPE versus PVW versus weighted residual methods to derive the element stiffness equations When is it easiest to use one method versus another What are the system requirements for use of each method 4 Describe the steps required to use the finite element method to find an approximate solution to a structural mechanics problem and the assumption that are introduced at each step Steps in the Finite Element Method 1 How do we decide on what element formulations to use to model a structural system and how to discretize the structural system 2 What are the PMPE and PVW What is the method of weighted residuals and how do we use these principles and methods to derive the stiffness equations for a truss element 3 How do we decide what form the approximate displacement functions that we use in the FE solution should have The Truss Element Formulation 1 What are the continuity and completeness requirements on the shape functions that we use for typical elements Why 2 Why do the shape functions we derived for 2node and higherorder elements satisfy these continuity and completeness requirements 3 For what load distribution is the trusselement formulation exact 4 How do we derive the trusselement stiffness equations using PMPE PVW and Galerkin s Method Triangular Continuum Element Formulations 1 What are the continuity and completeness requirements on the shape functions that we use for typical triangular elements Why 2 How do we derive shape functions to satisfy the continuity completeness requirements 3 Why do the shape functions we derived for 3node triangular element and higherorder triangular elements satisfy these continuity and completeness requirements 4 For what load distribution is the threenode triangular element formulation exact 5 How do we derive the continuumelement stiffness equations using PMPE 6 How do we compute effective equivalent nodal load vectors for quadrilateral elements 7 Write a matlab script to solve problems using triangular elements Modeling Distributed Loads 1 Derive an effective equivalent in the text by Logan load vector that represents the distributed load applied to an axial element Application ofthe Finite Element Method 1 Complete an analysis of a 1D structural system using the FEM 2 Evaluate the results displacement field stress field axial force field of the FEM analysis of the 1D system and comment on the error and comment on howthe solution can be improved by re meshing with the same number of elements with higherorder elements and with more elements

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