What is weak formulation in FEA?

What is weak formulation in FEA?

The weak form (1D) 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 do you derive a weak formulation?

Procedure for Generating Weak Forms

1. Write down the strong form of the equation.
2. Rearrange terms so that all are on one side of the equals sign, with zero on the other.
3. Multiply the whole equation by a test function ψ.
4. Integrate the whole equation over the domain Ω and apply the integrand sum rule to separate the terms.

Why is variational formulation referred to as weak formulation?

The variational formulation also known as weak formulation allows to find in a fast and simple way the solution to phenomena or problems modeled through PDEs, these when analyzed with the techniques or classical theory of PDE, it is very complex to find a solution that satisfies said equations.

What is weak from why it is called a weak form why weak form is desired in FEM?

Weak form is an alternate representation of the differential equation. The strong form imposes continuity and differentiability requirements on the potential solutions to the equation. The weak form relaxes these requirements on solutions to a certain extent.

Why is weak form important in FEM?

The weak form reduces the continuity requirements on the basis functions used for approximation which gives way to using lesser degree polynomials. This is done by converting the differential equation into an integral form which is usually easier to solve comparatively.

What is CST and LST elements?

Why CST & LST is called constant & linear strain triangle element? CST – Constant Strain Triangle – First order Triangle Element – 3 nodes per Triangle. LST – Linear Strain Triangle – Second order Triangle Element – 6 nodes in Triangle. In CST – Strain in the element won’t vary.

What is strong form and weak form in finite element analysis?

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 is the meaning of weak formulation Nptel?

What is the meaning of weak formulation? Solutions obtained are incorrect. The differentiability requirement on primary variable is decreased. The differentiability requirement on primary variable is increased. No Boundary conditions have to be satisfied.

What is strong form and weak form in FEM?

What is variational method in FEM?

Method of Weighted Residuals (MWR) and Variational Approach are two approaches in Finite Element Methods. Variational approach of finding displacements (unknowns in structural mech) basically employs the concept of minimizing the total energy of the body in a variational sense w. r. t. the displacements.

What is weak form efficient market hypothesis?

Weak form efficiency states that past prices, historical values and trends can’t predict future prices. Weak form efficiency is an element of efficient market hypothesis. Weak form efficiency states that stock prices reflect all current information.

Why is weak form called weak?

On the other hand a weak form states the conditions that the solution must satisfy in an integral sense. The governing equation is combined with the natural boundary conditions in an integral form. The order of derivatives are reduced to (n) and hence “weak” form. the resulted equation is called the weak form.