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    Finite Element Method An Introduction: Andriya Narasimhulu 9899518264

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    Ankit Sharma
    The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical analysis technique used to approximate solutions to boundary value problems by dividing the problem into smaller elements. It grew out of the aerospace industry's need for lightweight structural analysis. The key steps of FEM include discretizing the domain, selecting element types, deriving stiffness matrices, assembling equations, solving for unknowns, and interpreting results. Commercial FEM programs make this process easier but are less efficient than specialized programs.

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    Finite Element Method An Introduction: Andriya Narasimhulu 9899518264

    Uploaded by

    Ankit Sharma
    52 views18 pages
    The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical analysis technique used to approximate solutions to boundary value problems by dividing the problem into smaller elements. It grew out of the aerospace industry's need for lightweight structural analysis. The key steps of FEM include discretizing the domain, selecting element types, deriving stiffness matrices, assembling equations, solving for unknowns, and interpreting results. Commercial FEM programs make this process easier but are less efficient than specialized programs.

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    Introduction 1of2

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    The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical analysis technique used to approximate solutions to boundary value problems by dividing the problem into smaller elements. It grew out of the aerospace industry's need for lightweight structural analysis. The key steps of FEM include discretizing the domain, selecting element types, deriving stiffness matrices, assembling equations, solving for unknowns, and interpreting results. Commercial FEM programs make this process easier but are less efficient than specialized programs.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    52 views18 pages

    Finite Element Method An Introduction: Andriya Narasimhulu 9899518264

    Uploaded by

    Ankit Sharma
    The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical analysis technique used to approximate solutions to boundary value problems by dividing the problem into smaller elements. It grew out of the aerospace industry's need for lightweight structural analysis. The key steps of FEM include discretizing the domain, selecting element types, deriving stiffness matrices, assembling equations, solving for unknowns, and interpreting results. Commercial FEM programs make this process easier but are less efficient than specialized programs.

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    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    You are on page 1of 18

    1/30/2012

    narasimha.iitdelhi@gmail.com

    FINITE ELEMENT METHOD AN INTRODUCTION


    Andriya Narasimhulu 9899518264 narasimha.iitdelhi@gmail.com

    narasimha.iitdelhi@gmail.com

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    narasimha.iitdelhi@gmail.com

    narasimha.iitdelhi@gmail.com

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    narasimha.iitdelhi@gmail.com

    narasimha.iitdelhi@gmail.com

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    narasimha.iitdelhi@gmail.com

    narasimha.iitdelhi@gmail.com

    WHAT IS FEM?

    The finite element method is a numerical method for solving problems of engineering and mathematical physics. Useful for problems with complicated geometries, loadings, and material properties where analytical solutionscan not be obtained.
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    DISCRETIZATIONS

    Model body by dividing it into an equivalent system of smaller bodies or units (finite elements) interconnected at points common to two or more elements (nodes or nodal points) and/or boundary lines and/or surfaces.

    narasimha.iitdelhi@gmail.com

    HISTORY

    Grew out of aerospace industry. Post-WW II jets, missiles, space flight


    Need for light weight structures
    Required accurate stress analysis
    Paralleled growth of computers

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    INTRODUCTION
    Finite element analysis is a powerful tool that allows engineers to quickly analyze and refine a design.

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    INTRODUCTION
    FEA can be applied to problems involving: structural design

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    VIBRATIONS

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    HEAT TRANSFER

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    SHEET METAL PARTS

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    PRODUCT DESIGN

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    PRODUCT DESIGN

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    In a structural simulation, FEM helps tremendously in producing stiffness and strength visualizations and also in minimizing weight, materials, and costs FEM allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements.

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    FEA is extensively used in Aerospace industry, automobile industry, computer hardware development,

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    Obtain a set of algebraic equations to solve for unknown nodal quantity (displacement). Secondary quantities (stresses and strains) are expressed in terms of nodal values of primary quantity

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    ADVANTAGES Irregular Boundaries General Loads Different Materials Boundary Conditions Variable Element Size Easy Modification Dynamics Nonlinear Problems (Geometric or Material)
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    STEPS IN THE PROCESS


    Discretize and Select Element Type Select a Displacement Function Define Strain/Displacement and Stress/Strain Relationships Derive Element Stiffness Matrix & Eqs. Assemble Equations and Introduce B.C.s Solve for the Unknown Degrees of Freedom Solve for Element Stresses and Strains Interpret the Results
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    COMPUTER PROGRAMS Small Special Purpose ProgramsTruss


    Frame Plane Stress Heat Transfer

    Large General Purpose Program (Commercial)

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    PROGRAMS
    ALGOR ANSYS COSMOS/M STARDYNE IMAGES-3D MSC/NASTRAN SAP90 ADINA NISA
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    GENERAL PURPOSE PROGRAMS ADVANTAGES Easy input -preprocessor. Solves many types of problems Modular design -fluids, dynamics, heat, etc. Can run on PCs now. Relatively low cost. High development costs. Less efficient than smaller programs, Often proprietary. User access to code limited.
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