Finite Element Basic Concepts Formulation of Finite Elements Computer Implementation of FEM Course Coverage Where the CourseFits ! Computational.

 

hfuzz 100pt ootline hfill IFEM Ch 13 -- Slide olio hfill hSlide -25pt BoxedEPSF IFEM. Ch13. Slide01. eps scaled 600 ven yeIFEM.

 

hfuzz 100pt footline hfill IFEM Ch 13 -- Slide folio hfill hSlide -25pt BoxedEPSF IFEM. Ch13. Slide01. eps scaled 600 ven yeIFEM.

 

1 1Ð1 1Ð 2 TABLEOFCONTENTS Page ¤1. 1. 1Ð3 ¤1. 1. 1. 1Ð3 ¤1. 1. 2. Staticsvs. Dynamics. 1Ð4 ¤1. 1. 3. Linearvs. Nonlinear. 1Ð4 ¤1. 1. 4. 1Ð4 ¤1. 1. 5. FEMVariants. 1Ð5 ¤1. 2. 1Ð5 ¤1. 3. 1Ð7 ¤1. 3. 1. ThePhysicalFEM. 1Ð7 ¤1. 3. 2. 1Ð8

 

1 1Ð1 1Ð 2 TABLEOFCONTENTS Page ¤1. 1. 1Ð3 ¤1. 1. 1. 1Ð3 ¤1. 1. 2. Staticsvs. Dynamics. 1Ð4 ¤1. 1. 3. Linearvs. Nonlinear. 1Ð4 ¤1. 1. 4. 1Ð4 ¤1. 1. 5. FEMVariants. 1Ð5 ¤1. 2. 1Ð5 ¤1. 3. 1Ð7 ¤1. 3. 1. ThePhysicalFEM. 1Ð7 ¤1. 3. 2. 1Ð8

 

1 1Ð1 1Ð 2 TABLEOFCONTENTS Page ¤1. 1. 1Ð3 ¤1. 1. 1. 1Ð3 ¤1. 1. 2. Staticsvs. Dynamics. 1Ð4 ¤1. 1. 3. Linearvs. Nonlinear. 1Ð4 ¤1. 1. 4. 1Ð4 ¤1. 1. 5. FEMVariants. 1Ð5 ¤1. 2. 1Ð5 ¤1. 3. 1Ð7 ¤1. 3. 1. ThePhysicalFEM. 1Ð7 ¤1. 3. 2. 1Ð8

 

Introduction toFEM10 Introduction to FEM Superelements bottom up top down Two extremes Ð Slide2.

 

Introduction toFEM4 h4ÐSlide1 Introduction to FEM Computer Algebra Systems: What Are They Computer tools to help humans solve math problems.

 

Introduction toFEM15.

 

Introduction toFEM6 h6ÐSlide1 Introduction to FEM FEM Terminology degrees of freedom abbrv: DOF state primary variables: displacements in mechanics conjugate variables: forces.

 

Introduction toFEM17 Isoparametric Quadrilaterals Implementation Steps for Element Stiffness Matrix: 1. Construct Shape Functions in Quad Coordinates Chapter 18 is devoted.

 

Introduction to FEM A Beam is a Structural Member Designed to Resist Primarily Transverse Loads Ð Slide2.

 

Introduction toFEM11.

 

Introduction toFEM18 Magic Means Direct by inspection Do in 15 minutes what took smart people several months and less gifted, several.

 

Introduction to FEM h2ÐSlide1.

 

Introduction toFEM25 Role of the Assembler in a FEM Code Introduction to FEM Stiffness Matrices geometry element connectivity material fabrication freedom activity Assembler.

 

Remaining ASEN 5007 Schedule Today Solving FEM Equations descriptive only, no HW 12/2 Complete plane stress program Ch 27 demos 12/7.

 

Introduction toFEM21 Introduction to FEM The Three Basic Stages of a FEM Program Based on the Direct Stiffness Method : setting up the stiffness equations and solving for displacements.

 

Introduction toFEM17 Isoparametric Quadrilaterals Implementation Steps for Element Stiffness Matrix: 1. Construct Shape Functions in Quad Coordinates Chapter 18 is devoted.

 

Introduction toFEM15.

 

Introduction toFEM10 Introduction to FEM Superelements bottom up top down Two extremes Ð Slide2.

 

Introduction to FEM Multifreedom Constraintsux4 0uy9 0 6ux2 12uy2ux2 2ux4 ux6 0 25 x5 ux5 x3 ux3 2 y5 uy5 y3 uy3 2 0 Single freedom constraint examples Multifreedom constraint examples linear, homogeneous.

 

The 4-Node Bilinear Iso-P Quad Introduction toFEM1234 x ,y 11 x ,y 22 x ,y 33 x ,y 44 IFEMCh23 Ð Slide2.

 

Introduction to FEM h2ÐSlide1.

 

Introduction toFEM6 h6ÐSlide1 Introduction to FEM FEM Terminology degrees of freedom abbrv: DOF state primary variables: displacements in mechanics conjugate variables: forces.

 

Introduction toFEM27 Introduction to FEM The 3 Basic Stages of a FEM-DSM Program : defining the FEM model Processing : setting up the stiffness equations and solving for displacements Postprocessing.

 

Introduction toFEM28.

 

The 4-Node Bilinear Iso-P Quad Introduction toFEM1234 x ,y 11 x ,y 22 x ,y 33 x ,y 44 IFEMCh23 Ð Slide2.

 

Remaining ASEN 5007 Schedule Today Solving FEM Equations descriptive only, no HW 12/2 Complete plane stress program Ch 27 demos 12/7.

 

Introduction toFEM5 h5ÐSlide1 What Are MoM Members whose stiffness equations can be constructed by Mechanics of Materials MoM methods Can be locally modeled as 1D elements Introduction.

 

Introduction toFEM6 h6ÐSlide1 Introduction to FEM FEM Terminology degrees of freedom abbrv: DOF state primary variables: displacements in mechanics conjugate variables: forces.

 

Introduction toFEM27 Introduction to FEM The 3 Basic Stages of a FEM-DSM Program : defining the FEM model Processing : setting up the stiffness equations and solving for displacements Postprocessing.

 

Introduction toFEM4 h4ÐSlide1 Introduction to FEM Computer Algebra Systems: What Are They Computer tools to help humans solve math problems.

 

Introduction toFEM10 Introduction to FEM Superelements bottom up top down Two extremes Ð Slide2.

 

Introduction toFEM17 Isoparametric Quadrilaterals Implementation Steps for Element Stiffness Matrix: 1. Construct Shape Functions in Quad Coordinates Chapter 18 is devoted.

 

Topics in Chapter 7 General Modeling Rules Finite Element Mesh Layouts Distributed Loads NbN Lumping EbE Lumping Displacement BCs taking advantage.

 

Introduction toFEM9 h9ÐSlide1 Introduction to FEM Penalty Function Method Physical u6Recall the example structure under the homogeneous MFC 1 2 3 4 5 6 Ð Slide2.

 

Introduction to FEM h2ÐSlide1.

 

Introduction toFEM25 Role of the Assembler in a FEM Code Introduction to FEM Stiffness Matrices geometry element connectivity material fabrication freedom activity Assembler.

 

Introduction toFEM20.

 

Topics in Chapter 7 General Modeling Rules Finite Element Mesh Layouts Distributed Loads NbN Lumping EbE Lumping Displacement BCs taking advantage.

 

Introduction toFEM14.

 

Introduction toFEM19 Convergence Requirements for Finite Element Discretization : discrete FEM solution approaches the analytical math model solution in some sense.

 

Introduction to FEM Multifreedom Constraintsux4 0uy9 0 6ux2 12uy2ux2 2ux4 ux6 0 25 x5 ux5 x3 ux3 2 y5 uy5 y3 uy3 2 0 Single freedom constraint examples Multifreedom constraint examples linear, homogeneous.

 

Introduction toFEM16 Isoparametric Representation of Finite Elements Element geometry and displacements are represented by same set of shape functions iso same Introduction toFEMÐSlide2.