do question 2 only Consider a 1D linear finite element defin

do question 2 only

Consider a 1D linear finite element defined by the domain x_1^e lessthanorequalto x lessthanorequalto x_2^3 where x_1^e and x_2^e are node coordinates. Express the integral expression for the element force vector {f}_(2 times 1)^e components, f_1^e and f_2^3, in terms of the local element coordinate, 01 lessthanorequalto zeta lessthanorequalto 1, and node positions, x_1^e and x_2^e, using the following problem data Problem data: 0 lessthanorequalto x lessthanorequalto L, A(x) = 1, L = 1, E = 1, b(x) = 1/2 (1 - cos (2 pi x/L)), Use a 1 point numerical integration rule to approximate the integral expression results in problem 2. Express the results in terms of the node positions, x_1^e and x_2^e and problem 1 parameters.

Solution

10Analysis: The dataset prepared by the preprocessor is used as input to the finite element code itself, which constructs and solves a system of linear or nonlinear algebraic equations Kijuj = fi where u and f are the displacements and externally applied forces at the nodal points. The formation of the K matrix is dependent on the type of problem being attacked, and this module will outline the approach for truss and linear elastic stress analyses. Commercial codes may have very large element libraries, with elements appropriate to a wide range of problem types. One of FEA’s principal advantages is that many problem types can be addressed with the same code, merely by specifying the appropriate element types from the library.

2)In the FEM, the structural system is modeled by a set of appropriate finite elementsinterconnected at points called nodes. Elements may have physical properties such as thickness, coefficient of thermal expansion, density, Young\'s modulus, shear modulus and Poisson\'s ratio.So a node is also a point.However, a node is a point which is obtained when the domain is descritized and a mesh is generated . A node is also used to define finite element basis (trial) functions.