FEA Structural Analysis
FEA (Finite Element Analysis) Structural Analysis is a computational method used to predict how a structure will respond to various loading conditions. It involves breaking down a complex structure into smaller, more manageable elements to analyze stress, strain, and deformation. By simulating real-world conditions, FEA helps engineers optimize designs and identify potential failure points in structures.
5 Key excerpts on "FEA Structural Analysis"
eBook - ePubMechanical Engineering Design
Third Edition
- Ansel C. Ugural(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...17 Finite Element Analysis in Design * * The material presented in this chapter is optional and the entire chapter can be omitted without destroying the continuity of the text. 17.1 Introduction In real design problems, generally, structures are composed of a large assemblage of various members. In addition, the built-up structures or machines and their components involve complicated geometries, loadings, and material properties. Given these factors, it becomes apparent that the classical methods can no longer be used. For complex structures, the designer has to resort to more general approaches of analysis. The most widely used of these techniques is the finite element stiffness or displacement method. Unless otherwise specified, we refer to it as the finite element method (FEM). Finite element analysis (FEA) is a numerical approach and well-suited to digital computers. The method is based on the formulations of a simultaneous set of algebraic equations relating forces to corresponding displacements at discrete preselected points (called nodes) on the structure. These governing algebraic equations, also referred to as force-displacement relations, are expressed in matrix notation. With the advent of high-speed, large-storage capacity digital computers, the FEM gained great prominence throughout industries in the solution of practical analysis and design problems of high complexity. The literature related to the FEA is extensive (e.g., [ 1 – 5 ]). Numerous commercial FEA software programs are available, including some directed at the learning process. Most of the developments have now been coded into commercial programs. The FEM offers numerous advantages, including: 1. Structural shape of components that can readily be described. 2. Ability to deal with discontinuities. 3. Ability to handle composite and anisotropic materials. 4. Ease of dealing with dynamic and thermal loadings. 5. Ability to treat combined load conditions. 6...
eBook - ePub- Ansel C. Ugural(Author)
- 2022(Publication Date)
- CRC Press(Publisher)
...17 Finite Element Analysis in Design * DOI: 10.1201/9781003251378-20 17.1 Introduction In real design problems, generally, structures are composed of a large assemblage of various members. In addition, the built-up structures or machines and their components involve complicated geometries, loadings, and material properties. Given these factors, it becomes apparent that the classical methods can no longer be used. For complex structures, the designer has to resort to more general approaches of analysis. The most widely used of these techniques is the finite element stiffness or displacement method. Unless otherwise specified, we refer to it as the finite element method (FEM). Finite element analysis (FEA) is a numerical approach and well-suited to digital computers. The method is based on the formulations of a simultaneous set of algebraic equations relating forces to corresponding displacements at discrete preselected points (called nodes) on the structure. These governing algebraic equations, also referred to as force-displacement relations, are expressed in matrix notation. With the advent of high-speed, large-storage capacity digital computers, the FEM gained great prominence throughout industries in the solution of practical analysis and design problems of high complexity. The literature related to the FEA is extensive (e.g., [ 1, 2, 3, 4 and 5 ]). Numerous commercial FEA software programs are available, including some directed at the learning process. Most of the developments have now been coded into commercial programs...
eBook - ePubMechanics of Solid Polymers
Theory and Computational Modeling
- Jorgen S Bergstrom(Author)
- 2015(Publication Date)
- William Andrew(Publisher)
...In practice, finite element analysis (FEA) can be divided into two different categories: implicit and explicit simulations, see Table 3.3. FEA can also be used to study eigenfrequencies and eigenmodes of deformation for a component or system. Table 3.3 Comparison Between Implicit and Explicit FEA Implicit Analysis Explicit Analysis Solves the equilibrium equations at each time step Solves the problem using Newton’s law of motion Good for static problems Good for short duration dynamic problems Is numerically stable Is only numerically stable for small time increments If the FE software finds a solution, that solution is likely to have small numerical errors Often easy to find a solution, but care is needed to find a solution with small numerical errors Contact problems are sometimes difficult to handle Good at handling problems with contact As mentioned, one of the most difficult steps in an FE simulation is to specify the material model. A material model is here defined as a constitutive equation and a corresponding set of material parameters: FE software contains a library of different constitutive equations that can be chosen, but the material parameters are typically not provided and the selection of constitutive models that are available is typically targeted to metals. There are generally only a limited set of constitutive models that are suitable for predicting the deformation behavior of polymers. One way to get around this is to use an external user material subroutine (UMAT) to define the material behavior, see Chapter 10 for more details. 3.3 Review of Modeling Techniques Most polymer mechanics problems can be divided into two main categories: predictions of deformation behavior and predictions of failure events. A common approach is to start with a deformation analysis to determine the magnitudes and distributions of stress and strain, and then, if needed, use this information as part of a predictive failure analysis...
- Andy Choi(Author)
- 2018(Publication Date)
- Bentham Science Publishers(Publisher)
...The Basics The finite element method is a mathematical approach used to examine continua and structures. Typically, the problem at hand is too difficult to be resolved in a satisfactory manner using classical analytical means. The finite element process generates a lot of simultaneous algebraic equations, which are created and calculated on a digital computer. Finite element calculations are carried out on laptops, mainframes, and personal computers. Results are seldom precise. However, errors are reduced by processing more equations, and results accurate enough for engineering applications are attainable at reasonable costs. Finite element analysis examines a complex problem by redefining it as the summation of the solutions of a series of interrelated simpler problems. The first stage involves subdividing (that is, discretize) the complex geometry into a suitable set of smaller “elements” of “finite” dimensions. This forms the “mesh” model of the investigated structure when combined (Fig. 29). Fig. (29)) Schematic illustration of a dental implant. (A) Solid model; (B) Finite element mesh. Each element can undertake a specific geometric shape (that is, square, cube, triangle, tetrahedron, for example) with a specific internal strain function. The equilibrium equations between the displacements taking place at its corner points or “nodes” and the external forces acting on the element can be written using these functions, the actual geometry of the element, and a suite of boundary conditions such as constrain points. One equation for each degree of freedom will be created for each node of the element. In general, these equations are appropriately written in matrix form for utilization in a computer algorithm. From the above example, and as a whole, the finite element method models a structure as an assembly of small parts (elements). A simple geometry is used to define each element and therefore is much easier to examine than the actual structure...
- Saad A. Ragab, Hassan E. Fayed(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
...Preface Computational approaches to solving engineering problems have become essential analysis and design tools for engineers. The finite-element method is at the center of modern computer analysis techniques. Before embarking on using massive finite-element commercial software, engineers need to know how finite- element models are derived for the basic principles that are usually expressed as differential or integral statements. Having strong mathematical foundation of the finite-element method, engineering students will be better prepared to tackle complex problems. This textbook Introduction to Finite Element Analysis has evolved from the first author’s lecture notes for finite-element courses that were taught in the department of engineering science and mechanics (now biomedical engineering and mechanics) at Virginia Tech for the past 17 years. The book serves as an introduction to the finite-element method, and presents it as a numerical technique for solving differential equations that describe problems in civil, mechanical, aerospace, and biomedical engineering. It enables engineering students to formulate and solve finite-element models of practical problems and analyze the results. Although commercial finite-element software are not used in this book, it explains the mathematical foundation underpinning such software. Mastering the techniques presented in this book, students will be better prepared to use commercial software as practicing engineers. The book is intended for senior or first-year graduate students in engineering or related disciplines. Thus, mathematical rigor is not compromised but presented at a level consistent with the anticipated mathematics background required in most engineering curricula. The power and versatility of the finite-element method is demonstrated by a large number of examples and exercises of practical engineering problems...
