"The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling."
The study of how structures respond to stress and strain.
Mathematics for FEM: Fundamentals of calculus, linear algebra, advanced algebra, partial differential equations, and numerical methods. An understanding of mathematics is essential to develop a mathematical model of a problem that involves FEM.
Solid Mechanics: Statics, dynamics, elasticity, strength of materials, and theory of structures. These concepts are essential as they provide the structural basis for FEM.
Principles of Mechanics of Materials: Constitutive models and material properties for different materials including metals, composites, and polymers.
Continuum Mechanics: Continuum mechanics is the study of the behavior of continuous matter under the influence of various loads. This is the basis for developing FEM solutions.
Computer Programming: Knowledge of a programming language such as C or Fortran is useful as it enables users to develop their own FEM codes.
Mesh generation: The generation of a finite element mesh is the foundation of FEM; this ensures a smoother method of analysis.
Finite Element Methods and Algorithms: Various numerical methods and algorithms that are used in finite element analysis, including the variational and Galerkin methods.
Boundary Conditions: Setting boundary conditions that are consistent with the problem being solved.
Static Analysis: Linear, non-linear, and dynamic analyses in 1D, 2D, and 3D models, including modeling of static load and constraint conditions.
Dynamic Analysis: Transient, harmonic, random vibration analysis, and response spectrum analysis.
Structural Dynamics: Eigenvalue problems, mode shapes vibrations, and free vibration problems in mechanical systems.
Heat Transfer and Thermal Stress Analysis: Understanding how heat is transferred and studying the effect of heat sources on materials and structure.
Fatigue Analysis: Studying the life cycle of a material, how it responds to cyclic loading, and the effect of crack growth.
Optimization: How to optimize a particular design component, such as the geometry, the material used or the boundary conditions to achieve the desired outcome.
Multidisciplinary Analysis: The integration of multiple engineering disciplines, such as structural, thermal, and fluid analysis, in one simulation tool.
Static Analysis: The study of the behavior of a structure under a fixed load or boundary condition.
Dynamic Analysis: The study of the structural response to dynamic loads, such as vibrations, shock, and impact.
Modal Analysis: The study of the natural frequencies and modes of vibration of a system.
Heat Transfer Analysis: The study of heat transfer within and between structures.
Fluid-Structure Interaction Analysis: The study of the interaction between a flow of fluid and a solid structure.
Nonlinear Analysis: The study of the behavior of a structure under large deformation, high stress levels, and material yielding.
Fatigue Analysis: The study of the behavior of a structure under cyclic loading.
Buckling Analysis: The study of the behavior of a structure under compressive loads, which can lead to failure with minimal deformation.
Contact Analysis: The study of the interaction between two or more contacting surfaces.
Optimization Analysis: The study of the optimization of a structure's design, based on a set of desired performance criteria.
"Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential."
"The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems)."
"To solve a problem, the FEM subdivides a large system into smaller, simpler parts called finite elements."
"The FEM achieves space discretization by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points."
"The finite element method formulation of a boundary value problem finally results in a system of algebraic equations."
"The method approximates the unknown function over the domain."
"The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem."
"The FEM then approximates a solution by minimizing an associated error function via the calculus of variations."
"Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA)."
"Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential."
"The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems)."
"To solve a problem, the FEM subdivides a large system into smaller, simpler parts called finite elements."
"Space discretization is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points."
"The finite element method formulation of a boundary value problem finally results in a system of algebraic equations."
"The method approximates the unknown function over the domain."
"The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem."
"The FEM then approximates a solution by minimizing an associated error function via the calculus of variations."
"Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA)."
"Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential."