EGM4350 Florida International University Homework 1 1 EGM 4350 Finite Element Methods in Mechanical Engineering Fall 2021 semester Homework 1. Submission deadline: 11:59pm on Sunday September 26, 2021...

Finite Element Methods in Mechanical Engineering


EGM4350 Florida International University Homework 1 1 EGM 4350 Finite Element Methods in Mechanical Engineering Fall 2021 semester Homework 1. Submission deadline: 11:59pm on Sunday September 26, 2021 Penalty for late submission: 20% per day Problem 1. Consider a cable loaded statically by a sinusoidal distribution of transverse load: ? = ?�??? �?? ? �, with ?� = 10, ? = 3. The prestressing force is ? = 150 ?�?. The left-hand end is pinned, and there's no force applied at the right-hand end. Compute the approximate solution for the deflection of the wire from the Galerkin formulation. Consider a one-term approximation with the test function ?1 = ?, and the basis function ?1 = ??? � πx 2 ? �. a) Obtain the analytical solution of the problem. b) Compute the multiplier ?1and plot the analytical and numerical solutions. Compare analytical and numerical solutions. c) Compute the force residual ?? at ? = ?. d) Compute the balance residual ?? for the approximate solution: ?? = ? ?2??????? ??2 + ?(?) EGM4350 Florida International University Homework 1 2 Problem 2. Same data as in Problem 1. Compute the approximate solution for the deflection of the wire from the Galerkin formulation. Consider a one-term approximation with the test function ?1 = ?, and the basis function ?1 = ?. a) Obtain the analytical solution of the problem. b) Compute the multiplier ?1and plot the analytical and numerical solutions. Compare analytical and numerical solutions. c) Compute the force residual ?? at ? = ?. d) Compute the balance residual ?? for the approximate solution: ?? = ? ?2??????? ??2 + ?(?) Problem 3. Same data as in Problem 1. Compute the approximate solution for the deflection of the wire from the Galerkin formulation. Consider a one-term approximation with the test function ?1 = ??? � πx ? �, and the basis function ?1 = ??? � πx ? �. a) Obtain the analytical solution of the problem. b) Compute the multiplier ?1and plot the analytical and numerical solutions. Compare analytical and numerical solutions. c) Compute the force residual ?? at ? = ?. d) Compute the balance residual ?? for the approximate solution: ?? = ? ?2??????? ??2 + ?(?) EGM4350 Florida International University Homework 1 3 Problem 4. Consider a cable loaded statically by a uniform distribution of transverse load ? = ?� with ?� = 19, L = 15. The prestressing force is ? = 30 ? �?. The left-hand end is pinned, and there's a force ?? = 30 applied downwards at the right-hand end. Compute the approximate solution for the deflection of the wire from the Galerkin formulation and plot it to compare with the analytical solution. Consider a two-term approximation with the basis functions ?1 = ?, and ?2 = ?2 and the test functions ?1 = ?1, ?2 = ?2.