FEA - Linear Hyperbolic PDEs for Vector Unknown in 3D - Linear Elastodynamics

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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.

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

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

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, it talks about the gradient of the trial solution and the weighting function. Lastly, it discussed 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. 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.