Finite Element Analysis (FEA) — Boundary Conditions, Basis Functions, and Numerics

Current Status
Not Enrolled
Price
Free
Get Started

We begin this course with a discussion about boundary conditions. We discuss a pure Dirichlet problem using an example of a linear elastic bar. We then move on to developing higher-order polynomial basis functions for Lagrange polynomials and discuss some properties of Lagrange polynomials. We then derive the matrix-vector equations using quadratic basis functions. Finally, we discuss numerical integration and Gauss quadrature rules which help in solving the matrix-vector equations numerically.
This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

Recommended Courses

STRUCTURES
Learn Physics

Finite Element Analysis (FEA) — The Matrix-vector Form

STRUCTURES
Learn Physics

Finite Element Analysis (FEA) — Analysis of the Finite Element Method

Structures
Learn Physics

Finite Element Analysis (FEA) — Variational Principles

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

In this course, we derive the matrix-vector weak form which is used in the finite element method. We begin by deriving the matrix-vector form for a single general element and then proceed to derive it for the entire problem domain by assembling the matrix-vector forms for all the elements in the domain.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course discusses why and how the FEA works and what are the special properties of the FEA. The norms that represent the finite-dimensional trial solution will be discussed. The important properties of the finite element method – consistency and the best approximation - will be explained in detail. Later, we will discuss the Pythagorean Theorem. The Sobolev estimates and convergence of the FEM will be explained further. And lastly, we will talk about finite element error estimation.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course focuses on obtaining the weak form using Variational Methods. Further, it discusses potential energy or Gibbs Free Energy. We will talk about ‘Pi’ as free energy functional and how the extrema can be used to check equilibrium states. Next, we discuss the variation in ‘Pi’ with respect to the variation in the field. Then, we will see how the extremization of free energy functional is performed.