Finite Element Analysis (FEA) — Linear and Elliptic Partial Differential Equations for a Scalar Variable in Two Dimensions

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This course discusses the process of building two-dimensional problems for the linear and elliptic PDEs using a scalar variable. The strong and the weak form are discussed using constitutive relations and boundary conditions. Then, we talk about the gradient of the trial solution and the weighting function. Lastly, we discuss the matrix-vector weak form. This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

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Finite Element Analysis (FEA) — Lagrange Basis Functions and Numerical Quadrature in 1D Through 3D

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 will discuss the use of Lagrange Polynomials in the basis functions in 1 through 3 dimensions. The formula for the basis functions is first written in 2D and then in 3D. We will further talk about the Gaussian Quadrature for numerical integration. Lastly, triangular and tetrahedral elements are discussed using these basis functions.

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 will discuss how to solve linear, hyperbolic partial differential equations for an unknown vector in three dimensions and apply the findings to study linear elastodynamics. The problem is time-dependent and so are the boundary conditions. Apart from boundary conditions, we also need initial conditions to solve this class of problems. We discuss various time discretization methods and the Newmark family of algorithms used to solve time-dependent problems. We then write the time-discretized problem in its modal form and learn how to solve it. We end the course with a discussion about the stability analysis and amplification matrix for such problems.

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 parabolic problems. The problems that will be discussed are linear parabolic PDEs in three dimensions for a scalar variable. Physical problems such as unsteady heat conduction and unsteady mass diffusion are considered here.