Pascal’s Triangle for determining the appropriate displacement field in finite element analysis

For the convergence of solution in finite element analysis, the assumed displacement field should be isotropic . This is achieved if the components of the displacement field are complete polynomials. This is achieved by using PASCAL’s TRIANGLE. It is a technique of including the appropriate number of terms in the displacement model. It also gives … Read more

Shape functions for different elements used in finite element analysis

Shape functions or interpolation functions are functions used to represent behaviour of a field variable within an element. In finite element analysis we deal with different elements. The elements can be linear, quadratic, 8- noded, 9-noded etc. The shape function for these elements is required to be determined to draw a relationship between the nodal … Read more

Numerical Integration in Finite Element Analysis

NUMERICAL INTEGRATION Numerical Integration is of prime importance when we deal with Finite Element Analysis especially in case of ISOPARAMETRIC ELEMENTS. Gauss Quadrature formula is the most commonly used Numerical Integration schemes. In this method sampling points are located and weight factors are attached to it. The attached document carry sufficient examples to explain the … Read more

Shape Functions or Interpolation Functions

Simple Element Shapes

Shape Functions or Interpolation Functions In FEA we discretize the solution region into finite elements. To conduct the analysis we assume a displacement model to approximately indicate the variations of the displacement within the element. The polynomial chosen to interpolate the field variables over the element are called shape functions. Denoted by[N], they establish the … Read more

Vibration Analysis of Structures

model hammer

courtesy:Govardhana Rao Introduction to Vibration Analysis of Structures Civil engineering structures are always designed to carry their own dead weight, superimposed loads and environmental loads such as wind or waves. These loads are usually treated as maximum loads not varying with time and hence as static loads. In some cases, the applied load involves not … Read more

Structural Dynamics and Degree of Freedom


Structural dynamics and earthquake engineering 1. Define the concept of dynamic degree of freedom. Give some examples of single degree of freedom systems and multi degree of freedom systems. Answer: Dynamic degrees of freedom are a set of independent displacements/rotations that completely define the displaced position of the mass with respect to its initial position. … Read more