The finite element is a numerical technique for solving a set of different simultaneous algebraic equations with imposed boundary conditions for analyzing structures Usually the problem addressed is too complicated to be solved satisfactorily by classical analysis methods. The method was originally applied to the problems of structural mechanics, heat conduction, magnetic and electric fields, lubrication, and others. However, the finite element method is an approximate technique based on the solutions of the equations. Care must be taken to ensure that the approximations are appropriate. Complex, unsolvable structures are broken into simple, solvable structures through FEM. It is also defined as: “The process of dividing domain having an infinite number of degree of freedom into a structure having a finite number of degree of freedom”
In the finite element method, the actual continuum is represented as an assembly of subdivisions called finite elements. These elements are considered to interconnect at a finite number of joints called nodes. A finite element mesh represents combinations of nodes and elements. Since the actual variations of field variables like displacement, temperature, stress, etc. inside the body is not known; we assumed the variations of field variables inside the element, which can be approximated by a single function called Interpolation function or shape function. The shape functions are different in terms of field variables at nodes. When the field equations are assembled for the whole body, the unknowns will be nodal values of field variables
Once these are known, shape functions can be defined through any point. FEA involves building an accurate 2D or 3D geometry model of the component to be analyzed. The model is broken up into discrete elements with nodes at their corners. Material properties are assigned for all materials used in the part. Boundary conditions are used to model physical connections to the part by setting the appropriate degrees of freedom (DOF) for all boundary nodes. Each node has up to 6 DOF comprised of three for translation and three for rotation. Boundary conditions can also be used to model dynamic, thermal, fluidic, and electrostatic connections. This part of the modeling process is done with a CAD-like processor to the FEA software or geometry data that can be imported from the existing CAD modeling software which may be an easier way for people to work.
Once the geometry, materials and boundary conditions are set, the next step is to decide on the element type and analysis type and then run the FEA solver to solve thousands of simultaneous differential equations to obtain a physical displacement at each node. This strain data is used to compute stress data at each node. A graphical postprocessor is used to digest all of this data and display it superimposed over the geometry model of the part with color-coded stress contour lines.
Applications of Finite Element tools
- Static Analysis: deflections, stress, strains, forces, and energies.
- Dynamic Analysis: frequencies, deflections, stress, strain, forces, and energies.
- Heat Transfer Analysis: Temperature, heat fluxes, thermal gradients, and heat flow from convection.
- Fluid Analysis: Pressure, gas temperature, convection coefficients, and velocities
- In the automobile industry.