MEM427_Lecture_2_Direct_Method

MEM427_Lecture_2_Direct_Method - MEM427 Introduction to...

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Unformatted text preview: MEM427 Introduction to Finite Element Method cture #2 Lecture #2 Direct Method Matrix Method of Structural Analysis y Chapter 2 Direct Method Matrix Method of Structural Analysis 1 MEM427 Introduction to Finite Element Method Basic Steps of Finite Element Analysis 1. Pre processing Phase Discretization : The physical domain is divided into a finite number of elements; elements are connected at nodes Formulation : Variables such displacement, stress, and strain within each element are approximated by simple functions (called shape functions ) and are expressed in terms of variables at nodes l t E ti ti f h l t l t d b d Element Equations : Equations for each element are formulated based on the shape functions and expressed in terms of variables at nodes Assembly : Element equations are assembled, using equilibrium and mpatibility conditions the odes form the global equations compatibility conditions at the nodes, to form the global equations Boundary Conditions : Displacement/force boundary conditions are applied to the global equations to form the reduced global equations . lution hase 2. Solution Phase Reduced global equations are solved numerically to determine the nodal variables 3. Post processing Phase Chapter 2 Direct Method Matrix Method of Structural Analysis 2 Eleme nt variables are evaluated using nodal values and the shape functions MEM427 Introduction to Finite Element Method asic Steps of Finite Element Analysis 1. Discretization Basic Steps of Finite Element Analysis 2. Formulation 3. Derivation of Element Equations 4. Assembly 5. Application of Boundary Conditions Y X Chapter 2 Direct Method Matrix Method of Structural Analysis 3 3 D FE analysis of a wrench FE analysis of a 2 D truss MEM427 Introduction to Finite Element Method asic Steps of Finite Element Analysis Basic Steps of Finite Element Analysis 500 lb 500 lb Discretization : No discretization is Example: Analysis of a 2 D truss 3 ft 3 ft needed each truss member is an element and each joint is a node Formulation : Variables (stress , strain , 3 ft displacements u and v , etc.) within each element are either constant or linear hence no approximation is needed t ti l t ti Element Equations : Element equations can be easily derived from Mechanics of Materials formulae ssembly Formation of the global 2 6 in . 8 psi, 10 9 . 1 A E Assembly : Formation of the global equations is straightforward : Joint (Node) Number : Member (Element) Number nite Element Method, when applied to truss problems, Chapter 2 Direct Method Matrix Method of Structural Analysis 4 Finite Element Method, when applied to truss problems, is identical to the Matrix Method of Structural Analysis MEM427 Introduction to Finite Element Method Recall the Matrix Method C C Statically determinate...
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MEM427_Lecture_2_Direct_Method - MEM427 Introduction to...

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