Using finite element shape functions, derive the stiffness matrix for a two-node bar element with varying cross section

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Using Finite Element Shape Functions Derive The Stiffness Matrix For A Two Node Bar Element With Varying Cross Section 1 (68.16 KiB) Viewed 17 times

Using finite element shape functions, derive the stiffness matrix for a two-node bar element with varying cross section given by x - Xi A = A₁(1 − −¹¹) + Aj ti) x - Xi L L where A, and A, are the areas at the end nodes, x is the coordinate indicated below and L is the length of the element. The Young's modulus, E, is constant. To receive full credit, use the expression for the virtual work of the internal forces. 1 Spring 2022 q A₁ X = Xi L 9 Aj X = Xj X