Finite Element Analysis of a 2-D Linear static structure (Flat plate)
Using Matlab
Under the Guidance of
Er. Shishupal Singh
Er. Ranbir Mukhya
(Faculties of Mechanical Engineering Department)
Submitted by
Areeb Siraj
(CSJMA15001390296)
Gaurav Arya
(CSJMA15001390253)
Department of Mechanical Engineering,
University Institute of Engineering and Technology,
C.S.J.M University, Kanpur - 208024
Abstract
A finite Element method approach has been developed for structural analysis of various
industrial products. It helps to analyze and solve the problem of structural displacement due
to various internal and external forces. And it also helps in the calculation stresses and
strains. This method can be applied to typical MEMS structures such as beam, plate and
other complex structures.
The theoretical analysis of the finite element method is well established in the case of the
triangular or tetrahedral meshes. In this case we use 4-node rectangular mesh, for the
analysis of a flat plate of uniform thickness with the help of Matlab.
Our theory supported by the some numerical experiments, which are taken from various
engineering application, ranging from elasticity and in other forces and stress analysis.
CONTENTS
TITLE PAGE 1
ABSTRACT Error! Bookmark not defined.2
CONTENTS Error! Bookmark not defined.3
1. Introduction 4
2. Terminologies 5
3. Basic steps for solving structural problems using FEA 6
4. Problem Based on 4 node quad. Element for flat plate of uniform thickness 7
5. Formulation of Element Equations 8
6. MATLAB Code 11
7. Results 14
CONCLUSION 16
REFERENCES 17
Introduction
Finite Element Analysis (FEA) is a numerical method for solving problems of
engineering and mathematical physics. Typical problem areas of interest
include structural analysis, heat transfer analysis, fluid flow analysis etc. The finite
element method formulation of the problem results in a system of algebraic
equations. The method yields approximate values of the unknowns at discrete
number of points over the domain. To solve the problem, it subdivides a large
problem into smaller, simpler parts that are called finite elements. The simple
equations that model these finite elements are then assembled into a larger system
of equations that models the entire problem.
In the first step above, the element equations are simple equations that locally
approximate the original complex equations to be studied, where the original
equations are often partial differential equations (PDE). To explain the
approximation in this process, FEM is commonly introduced as a special case
of Galerkin method. The process, in mathematical language, is to construct an
integral of the inner product of the residual and the weight functions and set the
integral to zero. In simple terms, it is a procedure that minimizes the error of
approximation by fitting trial functions into the PDE. The residual is the error
caused by the trial functions, and the weight functions
are polynomial approximation functions that project the residual.
FEA as applied in engineering is a computational tool for performing engineering
analysis. It includes the use of mesh generation techniques for dividing a complex
problem into small elements, as well as the use of software program (in our case
MATLAB) coded with FEM algorithm.
FEA is a good choice for analyzing problems over complicated domains like cars and
oil pipelines, machinery parts, objects under stress etc. FEA simulations provide a
valuable resource as they remove multiple instances of creation and testing of hard
prototypes for various high fidelity situations. For instance, in a frontal crash
simulation it is possible to increase prediction accuracy in "important" areas like the
front of the car and reduce it in its rear thus reducing cost of the simulation.
The purpose of finite element analysis (FEA) is to reduce the number of prototypes
and experiments that have to be run when designing, optimizing, or controlling a
device or process.
https://www.academia.edu/39873017/Finite_Element_Analysi
s_of_a_2-D_Linear_Static_Structure_Flat_Plate_Using_Matlab
Thanks You
