Engineering
Finite Element Methods
Train on Finite Element Methods with 115 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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See a problem from Finite Element Methods before you begin.
Course topics
Course topics
Weak formulations, Galerkin projection, and variational structure
Reference elements, interpolation, and numerical quadrature
Global assembly and essential or natural boundary conditions
Stability, consistency, a priori error, and adaptivity
Time-dependent and eigenvalue finite-element systems
Nonlinear, constrained, and mixed formulations
Practice problems
Try a few Finite Element Methods problems, each with a hint.
- A bar on 0 ≤ x ≤ 3 has piecewise-constant axial rigidity EA=2 for 0<x<1 and EA=5 for 1<x<3 Free with an accountWeak formulations, Galerkin projection, and variational structure
- A uniform axial bar of length 2.0 m and constant rigidity EA = 80 MN is fixed at x = 0… Free with an accountWeak formulations, Galerkin projection, and variational structure
- A prismatic Euler-Bernoulli beam element has length L=2.4 m and local degree-of-freedom… Free with an accountWeak formulations, Galerkin projection, and variational structure
- A two-node Timoshenko beam element of length L=1.2 m has local degrees of freedom… Free with an accountWeak formulations, Galerkin projection, and variational structure
- A curved-sided isoparametric LST uses natural coordinates (r,s), with L₁=1-r-s, L₂=r… Free with an accountWeak formulations, Galerkin projection, and variational structure
- A four-node bilinear quadrilateral has parent coordinates (ξ,η) ∈ [-1,1]² and local… Reference elements, interpolation, and numerical quadrature
- A two-node Timoshenko beam element of length L=2 uses linear interpolation for… Reference elements, interpolation, and numerical quadrature
- A composite wall occupies 0 ≤ x ≤ 0.30 m and has unit area normal to heat flow Reference elements, interpolation, and numerical quadrature
- An axisymmetric annular region in the r-z plane is 1 ≤ r ≤ 2, 0 ≤ z ≤ 1 Reference elements, interpolation, and numerical quadrature
- A unit-square, unit-thickness bilinear quadrilateral is used in plane strain for an… Reference elements, interpolation, and numerical quadrature