Contents
What is weak form of differential equation?
Weak form – an integral expression such as a functional which implicitly contains a differential equations is called a weak form. • The strong form states conditions that must be met at every material point, whereas weak form states conditions that must be met only in an average sense.
What are weak & strong form words?
Grammatical words are words that help us construct the sentence but they don’t mean anything: articles, prepositions, conjunctions, auxiliary verbs, etc. That weakened form is called “weak form” as opposed to a “strong form”, which is the full form of the word pronounced with stress.
What are the weak and strong forms of the finite element method?
After a long break I am back with a new interesting post about the Weak and Strong forms in the Finite Element Method! The mathematical models of heat conduction and elastostatics covered in Chapter 2 of this series consist of (partial) differential equations with initial conditions as well as boundary conditions.
Which is the best method for numerical integration?
1. Multiply by weighting function w 2. Integrate over the domain 3. Discretize and sum the contributions of each element in domain 5/6/2015 Adrian Egger | FEM I | FS 2015 5 From Strong to Weak form II Apply the divergence theorem: Equivalent to integration by parts in 1D 5/6/2015 Adrian Egger | FEM I | FS 2015 6 Beam Theory: Weak form
What is the Galerkin method for finite elements?
Galerkin approach for equations (1), (4), (5): 1. Multiply by weighting function w 2. Integrate over the domain 3. Discretize and sum the contributions of each element in domain 5/6/2015 Adrian Egger | FEM I | FS 2015 5 From Strong to Weak form II Apply the divergence theorem: Equivalent to integration by parts in 1D
Why does the stiffness matrix require an integral?
The computation of the stiffness matrix and load vectors requires the evaluation of one or more integrals depending on the dimension of the requested analysis. Why not analytical evaluation of the integral? Analytical solution not always feasible Analytical solution takes too much time to compute No guarantee that numerical issues are removed