03-08-2012, 04:20 PM
FINITE ELEMENT METHOD
Introduction to FEM.pdf (Size: 1.88 MB / Downloads: 94)
Definition
•FEM is a numerical technique to find the field variables.
•It is important technique that is used in CAD mainly for the modification of design part.
•The field variable is a basic parameter that can be measured and its derivatives are important for the modification of the design.
•For example displacement field & its derivatives like strain and hence stress is important for modification of design. Other field variable is temperature, magnetic field & so on.
INTRODUCTION
The finite element method (FEM), sometimes referred to as finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering.
Simply stated, a boundary value problem is a mathematical problem in which one or more dependent variables must satisfy a differential equation everywhere within a known domain of independent variables and satisfy specific conditions on the boundary of the domain.
Boundary value problems are also sometimes called field problems.
The field is the domain of interest and most often represents a physical structure.
The field variables are the dependent variables of interest governed by the differential equation.
The boundary conditions are the specified values of the field variables (or related variables such as derivatives) on the boundaries of the field.
Depending on the type of physical problem being analyzed, the field variables may include physical displacement, temperature, heat flux, and fluid velocity to name only a few.
APPROXIMATE METHODS
Analytical methods are not suitable for complex problems
Complexity can be due to geometry, material properties, complex boundary conditions
Hence, approximation methods are used
The Principle of Minimum Potential Energy (PMPE)
At the equilibrium the system will have minimum potential energy.
Of all the possible displacement functions that are sufficiently smooth (for compatibility) and which satisfy the geometric boundary conditions of the system, the set that corresponds to the stable static equilibrium of the system is the one that minimizes the potential energy functional of the system.