Expression of element stiffness matrix for 2d truss problem

Question

Answer the following questions in detail.

Question 1) Why are the polynomials most commonly used as interpolation functions in FEA?

Question 2) Explain the terms ‘compatibility’ and ‘completeness’ in relation to FEA.

Question 3) What are the various sources of errors in FEA, resulting it into an approximate method?

Question 4) What are the various factors on which the selection of type of element depends in FEA?

Question 5) Explain Jacobian matrix in detail.

Question 6) Write down the principle of minimum potential energy.

Question 7) What do you mean by LST element?

Question 8) Write down the properties of a stiffness matrix.

Question 9) What do you mean by axisymmetric element?

Question 10) Provide the stiffness matrix equation for an axisymmetric triangular element.

Question 11) Using any method, derive an expression of element stiffness matrix for a 2D truss problem.

Question 12) Describe in detail the Galerkin approach used in FEA.

Question 13) Derive a shape functions for isoparametric rectangular quadratic element using any method.

Question 14) Describe the general assembly method in which an element stiffness matrix is converted to global stiffness matrix.