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Finite Element Analysis

Finite element analysis (FEA) is a numerical analysis method used for solving a multitude of engineering problems related to structural analysis and fluid flow.

From: Human Orthopaedic Biomechanics, 2022

Related terms:

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Applications—Solid Mechanics Problems

Zhuming Bi, in Finite Element Analysis Applications, 2018

8.5 Summary

FEA was developed originally for numerical solutions of complex problems in solid mechanics. FEA is by far the most widely used and versatile technique for simulating deformable solids. This chapter gives an overview of the physical and mathematic background required to understand the FEA implementation for solid mechanics' problems. The physical behaviors of mechanical structures or systems are analyzed, and the minimum potential energy principle is used to develop element models. The procedures for FEA modeling are discussed for a few of classic solid mechanics' problems such as truss structure, plane stress, plane strain, modal analysis, as well as fatigue analysis.

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Computer-aided engineering findings on the physics of tire/road noise

Laith Egab, in Automotive Tire Noise and Vibrations, 2020

10.2.2.2 Energy finite element analysis

EFEA is a finite element-based computational method for high frequency vibration and acoustic analysis [16]. The EFEA applies finite element discretization to solve the governing differential energy equations. The primary variable in EFEA is defined as the time averaged energy density over a period and space averaged energy density over a wavelength.

The EFEA is compatible with low frequency FEM models since it can use an FEM database. This permits modeling flexibility and cost-saving as one FE model can be applied to both low and high frequency analysis. The prediction of a spatially varying energy level within a structural subsystem is available with the EFEA computation. The postprocessing of EFEA results also provides straight-forward visualization of the energy flow in a system, which is convenient for diagnoses and control of noise propagation.

EFEA can be applied to model highly damped or nonuniformly damped materials, and to model distributed masses as well as multipoint power input. Due to the utilization of the finite element technique, EFEA also has the other advantages that traditional FEM does not have. It can be easily applied to irregular domains and geometries that are composed of different materials or mixed boundary conditions.

Although SEA models result in a few of equations which are easy to solve, they cannot be developed from CAD data, local damping cannot be accounted for, and the model development requires specialized knowledge. In contrast, EFEA offers an improved alternative formulation to the SEA for simulating the structural-acoustic behavior of built-up structures. It is based on deriving governing differential equations in terms of energy density variables and employing a finite element approach for solving them numerically. There are several advantages offered by EFEA. These advantages include the generation of the numerical model based on geometry; spatial variation of the damping properties can be considered within a particular structural member; the excitation can be applied at discrete locations on the model, and EFEA can be applied to the high frequency range, which benefits the large community of FEA users. These unique capabilities make the EFEA method a powerful simulation tool for design and analysis.

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Finite element modelling of foam deformation

NJ Mills, in Polymer Foams Handbook, 2007

6.1.1 FEA packages

Finite element analysis (FEA) is used to find the stress distribution for complex geometries. This chapter explores the background to foam material models in FEA; other aspects of FEA are covered in texts such as Shames and Dym (1985). Experiments to validate the models will be critically examined. Further examples of use of FEA occur in the case studies (Chapters 9, 13, 14, 16, and 21) and the analysis of foam indentation (Chapter 15).

The choice of FEA package may be determined by cost. ABAQUS, widely available in universities, provides detailed explanations of the foam models. Updates, usually on an annual basis, have changed the foam models; consequently the pre-2002 modelling of crushable foams is largely ignored here. Other FEA packages, such as LS-DYNA or RADIOSS, offer a wide range of foam material models, but give little information on their origin or internal working. The automotive industry uses FEA for the design of car bodies, and the modelling of occupant protection with rigid foam padded components. It is an advantage if the same FEA programme can model the deformation of the steel structure, the rigid foam padding, and the occupant is used !