Question

1. What is stress discontinuity?
2. What is the difference between averaged and unaveraged stresses?
3. What is the purpose of determining structural error?
4. What is convergence as it is applied to the computation of analysis results?
5. What is stress singularity?
6. What are the methods to identify the stress singularity?
7. Why some models have stress singularities?

Answer 1

Stress Discontinuity : Structures usually contain region where abrupt change in geometry, material, or loading occur. These regions are known as discontinuity areas, and the stress associated with them are called discontinuity stress.

In these case, the real fracture strength of material is always lower than the theoretical value because most materials contain small cracks or contamination.

Causes-

1)Geometric discontinuities cause an object to experience a local increase in the intensity of a stress field. Examples of shapes that cause these concentrations are cracks, sharp corners, holes, and changes in the cross-sectional area of the object. High local stresses can cause objects to fail more quickly, so engineers must design the geometry to minimize stress concentrations.

2) Due to discontinuities in applied loads.

3) Material discontinuities which may occur while manufacturing.

Unaveraged Stress: Unaveraged stress means raw or actual stress at a point or node. It means ,at a point or node there may be four different stresses shared by four quadrants. The reason of different stresses at one node is ,different element stiffness for different element geometry or different applied load.If the C.G. of the elements are at different locations in the fea model, then different internal stresses will induced.

Averaged Stress: Averaged stresses have only one value at each node, averaging the all available elemental stresses at a node. Mathematically , it can be said that it is integrated value.

Structural Error: It is an error that permeates the entire conduct of the trial from beginning to end , and affects the framework within which the trial models proceeds.Finite Element software is typically used for modeling and analyzing the behaviour of a structure When using FE software, I the solution obtained is an approximate for many reasons.So to calculate the exact results we determine the structural error.

Convergence : If the error gets reduced at every step, then we can say that simulation is converging. In FEA Its associated with implicit method. If we consider a nonlinear static analysis, solver makes sure that every step equlibrium condition is satisfied. That means externally applied force( R) must equal to internal nodal force ( F). But in nonlinear analysis in single step it cannot be achieved. Every step iteration takes place to update tangent stiffness matrix by implicit method to make sure that R==F. or R-F=0. But achieving R-F=0 is quiet difficult. Hence ,we give some tolerance value, for example R-F=0.001. That means solver will iterate the process ( tangent stiffness matrix gets updated ) untill R-F=0.001. If this delta reduces every iteration then we say that simulation is converging. If it increases then it is said to be diverging. That means results are deviating from actual results.

Stress Singularly :

A stress singularity is a point of the mesh where the stress does not converge towards a specific value. As we keep refining the mesh, the stress at this point keeps increasing. Theoretically, the stress at the singularity is infinite.

To identify stress singularities we focus on these points:Typical situations where stress singularities occur are the appliance of a point load, sharp corners, corners of bodies in contact and point fixtures.

Some models have stress singularity because in some models stress does not converge towards a specific value when the basic elements dimension is reduced.