What is the meaning of weak formulation in FEA?
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain “test vectors” or “test functions”. …
What are weak and strong forms?
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.
How do you derive the weak form of PDE?
Procedure for Generating Weak Forms The general procedure for expressing the weak form of a PDE is as follows: Write down the strong form of the equation. Rearrange terms so that all are on one side of the equals sign, with zero on the other. Multiply the whole equation by a test function ψ.
What is strong form and weak form in FEM?
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 the weak forms?
Weak forms are syllable sounds that become unstressed in connected speech and are often then pronounced as a schwa. In the sentence below the first ‘do’ is a weak form and the second is stressed.
What is a strong form?
DEFINITIONS1. a pronunciation some words have when they are stressed, as opposed to when they are not stressed. For example, the word ‘at’ is pronounced with the strong form in the sentence ‘What are you looking at? ‘ Synonyms and related words.
What is weak form method?
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.
How is weak form used in finite element analysis?
This is the central idea of finite element method and it comes naturally from weak form. It is weak form method, that actually gives birth to the finite element formulation as we know it today. Weak form method manipulates the governing differential equation to reduce its order.
Is the weak form the same as the strong form?
To develop the finite element formulation, the partial differential equations must be restated in an integral form called the weak form. The weak form and the strong form are equivalent! In stress analysis the weak form is called the principle of virtual work.
How are weak forms constructed in the FEM?
The weak forms involve weight functions and trial solutions for the temperature, displacements, solute concentrations and so on. In the FEM, the weight functions and trial solutions are constructed by subdividing the domain of the problem into elements and constructing functions within each element.
How is the weak form used in mechanics?
In Mechanics the weak form is the same as principle of virtual work. In this form it is used to construct to approximate solutions to strong form. Sometimes the weak form makes more physical sense than the strong form. An example is the vibration of the string.