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Discretization of Physical Domains
Published in Guigen Zhang, Introduction to Integrative Engineering, 2017
Knowing that polynomial-based approximate solutions can sometimes provide very satisfying solutions to differential equations, one may wonder if such an approximate-solution-finding procedure based on polynomial functions can be handled by a computer program. Finite element method (FEM), which is also known as finite element analysis (FEA), is exactly one such computerized numerical procedure for finding approximate solutions to a wide range of scientific and engineering problems. Although the term finite element was coined by Ray W. Clough in 1960, the concept of using framework method and polynomial interpolations was first introduced by Alexander Hrennikoff and Richard Courant in the 1940s for solving structural engineering problems. Since 1960, the field of finite elements has witnessed many significant leaps, moving from solving problems of solid mechanics, fluid flow, heat transfer, and nonlinear and large deformations, to dealing with issues like mass transport, electricity and electronics, chemical reactions, and electrochemistry. Lately, it is moving to tackle problems of multiphysics and multiscale natures, thanks to the rapid advances in computer sciences and engineering and to the drastic explosion of computational powers and capabilities.
Application of Simulations in Structural Design
Published in Ram S. Gupta, Principles of Structural Design, 2020
However, with the advent of computing, mathematical modeling, instead of physical modeling, has become a convenient tool of analysis. More physics-based methods such as finite element methods (FEMs), or finite element analysis (FEA), give engineers the ability to assess the influence of relevant variables in a virtual environment and solve complex real-life designs. Through visualizing the effect of a wide range of variables in a virtual design environment, civil engineers can narrow the scope of field investigations, save considerable time and cost on projects, and move more quickly to the ground breaking stage.
Introduction
Published in Xiaolin Chen, Yijun Liu, Finite Element Modeling and Simulation with ANSYS Workbench, 2018
The finite element method (FEM), or finite element analysis (FEA), is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into smaller and manageable pieces. Application of this simple idea can be found everywhere in everyday life (Figure 1.1), as well as in engineering. For example, children play with LEGO® toys by using many small pieces, each of very simple geometry, to build various objects such as trains, ships, or buildings. With more and more smaller pieces, these objects will look more realistic.
Finite Element Analysis of Graphene Oxide Hinge Structure-based RF NEM Switch
Published in IETE Journal of Research, 2023
Rekha Chaudhary, Prachi Jhanwar, Prasantha R. Mudimela
In our work, FEM based tool COMSOL Multiphysics has used to perform NEM switch simulations. The modelling of finite element analysis (FEA) is accomplished in three steps: Pre-processing, Solver, and Post-processing [25]. In the pre-processing step, modelling of the structure is done. Pre-processing involves some sub-steps like the creation of geometry, assigning the material, selecting the physics, setting up the physics, and applying boundary conditions. Subsequently, the meshing of the device takes place in which the structure is divided into several finite elements. Then set of algebraic equations is solved. These equations provide nodal solutions related to physics. All the solutions of mathematical equations and finite element formulation occur behind the screen in the software. In COMSOL Multiphysics, two methods named segregated step method and fully coupled methods are used to obtain the model solutions. After generating the solutions, post-processing allows the user to evaluate and plot the results.
Evolution of different designs and wear studies in total hip prosthesis using finite element analysis: A review
Published in Cogent Engineering, 2022
Chethan K N, Shyamasunder Bhat N, Mohammad Zuber, Satish Shenoy B
Finite Element Analysis (FEA) is a numerical method extensively used to solve a variety of complex physical problems. FEA assumes a complex physical domain as a collection of many simple domains with linear or nonlinear attributes (material, geometry, loads, etc.). The fundamental governing differential equation of the physical system is brought down into a set of algebraic equations solved numerically to obtain the solution for non-linear, complex physical systems. With advantages over experimentation and analytical methods, FEA has the potential and versatility to be applied indisputably in all fields of engineering. These techniques are extensively used for solving multi-physics problems in the field of automobiles, aeronautical, and other structural and fluid dynamic applications.
Numerical analysis of railway substructure with geocell-reinforced ballast
Published in Geomechanics and Geoengineering, 2022
Amninder Singh Nayyar, Anil Kumar Sahu
Meshing is a procedure of dividing a part of the finite element model into small fragments. Mesh can be triangular, rectangular or square. For this study, in all numerical models, the element type of ballast mesh was C3D10I, a 10-node general purpose tetrahedron with improved surface stress formulation was considered. Tetrahedral shaped mesh has been selected to incorporate the effect of interlocking between granular ballast materials (Leshchinsky and Ling 2013b). For modelling of sleepers, geocell and clay, mesh element type C3D8R, an 8-node linear brick, reduced integration, hourglass control, was considered. Similarly, for rail element type C3D4, a 4-node linear tetrahedron, for meshing was taken. All components except the clay subgrade (coarsely modelled) were modelled finely. The optimum size of mesh was selected after the process of mesh convergence. Mesh convergence is the procedure in which it is verified that any further decrease in the size of mesh does not lead to the drastic change in the results.