In today’s world, the development of products is carried out in a systematic manner so as to create high-quality products effectively and efficiently. A product may have various requirements that are evaluated for different solutions to unify the development procedures. Product analysis is carried out at the end for the verification of the product and assists engineering designers to simulate the behavior of the product for further screening. Product analysis has become an important part of the product development process as it helps in the prediction of the final product behavior. One of the most important ways for product analysis is Finite Element Analysis.
Finite Element Analysis (FEA) is a numerical method for solving the problem of mathematical and engineering physics. It is used for solving complex geometries, material properties, and loadings where analytical solutions are very difficult to obtain. It is a way to simulate loading conditions to determine the design’s response to those conditions. It is modeled using discrete building blocks called elements. Each of these elements has an exact equation that represents the response to a particular load. FEM has become a powerful tool for solving differential equations and integral differential equations.
The final element method was first used by academic and industrial researchers in the 1950s for evaluating the suspension bridges and steam boilers. Since then it has grown in function and has been used for reducing the amount of prototype testing. It allows multiple simulation scenarios for testing that are used for cost and time savings. It extends reduced testing and redesign costs to shorten the product development cycle. It identifies safety issues or any irregularities in the development of the product. This process is helpful in finding design shortcomings before any future litigations. Designers are increasingly using it with CAD programs to allow solid modeling and mesh generations.
Finite element analysis is applied by businesses in engineering such as aerospace, civil, automotive, and mechanical, etc. It is used to analyze the fluid flow for structural and stress analysis for static and dynamic equations. Modern engineers are also using this process for analyzing the fluid flow and heat transfer in technical and industrial equipment. It is helpful in analyzing electromagnetic fields, soil mechanics, acoustics, and biomechanics.
In the method of finite element analysis, the accuracy of the solution is determined in terms of the refined element mesh. There are generally two methods for mesh refinement. First is h-refinement where an increasing number of elements are used to design a particular structural domain. Second is p-refinement where interpolation functions are increased by using the order of the polynomials. The refinement is done to estimate the sequential solutions that show the exact solution.
In this approach, solutions of the equations are converted into small finite segments. These elements are then further assembled to obtain an overall system of linear algebraic equations. Here is the general process of linear static structural analysis.
The first thing in the finite element method is to divide the solution into small elements so that the structure can be modeled. It is done after deciding the type, number, size, and arrangement of the elements in 1D, 2D, 3D, or axis symmetry. This is followed by the selection of a proper interpolation or displacement model as the structure of the model is very difficult to predict. It is done by assuming a solution from a computational point of view.
Further, strains and stresses are derived from the displacement model within each element by using Hooke’s law and strain-displacement relationship. As the displacements within each element are unknown variables, the compatibility equations within the element are automatically satisfied. The assumed displacement model is also helpful in deriving the load vector and the stiffness matrix by using the various variational principle. The next step in the process is to assemble the elemental equations to derive the overall equilibrium equations. The individual element stiffness matrices and load vectors are assembled in a systematic order for the overall equilibrium equation. The assembly of stiffness is carried out only on elements sharing a particular node. The process of finding the appropriate location for each of the individual element matrix in the global matrix is called the Direct Stiffness Method.
The next step in the finite analysis method is the imposition of boundary conditions in contact problems. After the incorporation of boundary conditions, the equilibrium equations are expressed. The element stresses and strains are further computed by using the equations of solid or structural mechanics.
Finite element analysis can readily handle the complex geometry and types of analysis. It can easily provide the results for vibration analysis, fluid analysis, heat transfer, transients, and no-linear. It can also handle complex loadings such as node-based loading or point loads, time or frequency-dependent loading, and element-based loading for estimating
pressure, thermal or inertial forces. The finite element method can model large displacements and rotations. It can also describe special material effects like swelling, creeping, plasticity, and temperature-dependent properties. It is very useful in handling the complex restraints for analyzing the intermediate structures and non-isotropic materials such as orthotropic and anisotropic materials.
In addition to the above advantages of the finite element method, there are numerous shortcomings as well. The finite analysis method is an approximate mathematical model of a system and a specific numerical result is derived from specific problems. This results in a general closed-form solution to examine the response to changes in various parameters. It requires vast experience and knowledge to construct a genuine finite system model. Further, it accumulates the error and rounds off most of the digits. It is susceptible to modeling errors by choosing a poor type of element. It can distort elements and sometimes geometry is not perfectly modeled. Finite analysis modeling requires a selection of proper mesh size and there is greater unwanted data. Greater memory and high-speed processors are required to carry out the analysis and are incapable of handling incompressible fluids.
There are many commercial finite element modeling packages available in the market. Some of these are ADINA, SOLIDWORKS, ABAQUS, ALGOR, ANSYS, C-MOLD, LS DYNA, etc.
ANSYS is one of the complete software packages used by engineers to analyze structural, thermal, and fluid engineering. It is also used to analyze the low and high-frequency electromagnetics. It is majorly used for electronics analysis in aerospace engineering, heavy equipment analysis in automotive engineering, microelectromechanical systems in biomedical engineering, and in bridges and buildings.
The finite element analysis method is increasingly used to obtain the solution for structural mechanics problems. It offers easy visualization of the machinery and equipment and is applicable to real-life problems of varied physical domains. One of them is the aerospace industry. The finite element analysis is used for the structural analysis in the aerospace industry. It is used for analyzing mode shapes, natural frequencies, and aero-servo-elastic studies. It is also used in aerodynamics and for analyzing natural frequencies.
Finite element analysis can be used to enhance the optimization and dependability of insulated design in high voltage equipment. It is extensively applicable in the complex configuration of dielectric insulating materials and electrodes. Finite element analysis can provide an equipotential field plot for a high voltage transformer and can assure the minimization of stray losses in electrical machines. One of the preferred processes for installing a thermal wire bonding between a lead frame and a semiconductor chip is the thermosonic wire bonding. It is connected by a metal wire. Wirebonding technology is a very complex task and works within certain boundaries and specifications, These designs have to meet the objective of lower mass, inertia, and higher dynamic stiffness. In such technologies, finite element analysis helps in analyzing the dynamic rigidity of the system.
It is highly crucial to identify the physical behaviors like fluid flow, strength, and transfer capability of complex objects. It is also useful in understanding the optimal design and predicting the behavior and performance of the design. It is considered as an important mathematical method for analyzing problems of mathematical and engineering physics. It is applicable to problems with complex loading, material properties, and geometries. Though stress analysis of trusses and beams can be analyzed by finding an analytical solution while finite element analysis is utilized in the situation where the designs are very complex. It is highly required for the situation where the accuracy is essential and to predict what’s going to happen when the product is used.