Question

Com derive the mathematical expressions of the shape functions for a 1d element having 4 nodes

Answer 1

Answer:

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. ... In this work linear shape functions are used. For three-dimensional finite element simulations it is convenient to discretize the simulation domain using tetrahedrons, as depicted iShape Functions: Shape functions are the polynomials meant to describe the variation of primary variable along the domain of element. Value of shape function of particular node is one and is zero to all other nodes. Sum of the derivative of all the shape functions for a particular primary variable is zero.