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Chapter 1. Introduction: This Course Consists of Three Parts

This course covers computational structural mechanics using the finite element method (FEM) to solve linear statics problems. It consists of three parts: finite element formulation, discretization techniques, and computer implementation. Specifically, it will spatially discretize physical systems using the displacement-formulation FEM and solve the discrete models using the stiffness method. The role of FEM is to bridge the idealized mathematical model and the discrete solution through discretization and solution of the discrete model.

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111 views9 pages

Chapter 1. Introduction: This Course Consists of Three Parts

This course covers computational structural mechanics using the finite element method (FEM) to solve linear statics problems. It consists of three parts: finite element formulation, discretization techniques, and computer implementation. Specifically, it will spatially discretize physical systems using the displacement-formulation FEM and solve the discrete models using the stiffness method. The role of FEM is to bridge the idealized mathematical model and the discrete solution through discretization and solution of the discrete model.

Uploaded by

sakeriraq81
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ME 478 FINITE ELEMENT METHOD

Chapter 1. Introduction
This course consists of three parts

1. Finite element formulation


2. Discretization techniques
3. Computer implementation of FEM

Where the course fits

The field of mechanics is divided into three parts


Theoretical
Applied
Computational

Computational mechanics can be distinguished according to the


physical focus of attention
Particle
Micromechanics
Solids and structure
Fluids
Coupled systems

Computational Solid and Structural Mechanics (CSM)

Linear
Statics
Nonlinear
CSM
Dynamics
1.1
For the numerical simulation on the computer we must now choose
a spatial discretization method:

Finite Element Method


Finite Difference Method
Boundary Element Method
CSM Linear Statics
Finite Volume Method
Spectral Methods
Mesh-Free Methods

CSM Linear Statics by FEM

Having selected the FEM for discretization, we must next pick


a formulation and a solution method:

Displacement
Equilibrium
Formulation of FEM Model
Mixed
Hybrid

Stiffness
Solution of FEM Model Flexibility
Mixed

1.2
Summary: This Course Covers

Computational Structural mechanics

Linear statics problems

Spatially discretized by displacement-formulation FEM

Solved by stiffness method

Role of FEM

Idealization Discretization Solution

Physical athematica Discrete Discrete


System Model Model Solution

Solution Error

Discretization +Solution Error


Modeling + Discretization +Solution Error

1.3
The Idealization Process

Physical Model

Idealization

Matematical Model

1.4
EXAMPLES
ALUMINUM/EPOXY BIMATERIAL SPECIMEN IN BENDING

1.5
RIGID PUNCH ON AN ELASTO-PLASTIC SUBSTRATE

THERMAL INDUCED DEFORMATION OF A MICRO MIRROR

1.6
SINGLE CRYSTAL SILICON PLATE WITH SQUARE HOLE

LOADED IN TENSION

1.7
CRACK PROPAGATION OF A PMMA T-STRUCTURE SPECIMEN

LOADED IN TENSION

CRACK KINKING AND PROPAGATION IN A SILICON/GLASS

MICRO ACCELEROMETER PACKAGE

1.8
WHAT NOT TO DO

1.9

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