Answer Happy

Finite Element Methods HW #7 Question 1: For each of the following differential equations and stated boundary conditions, obtain a one-term solution using Galerkin's method of weighted residuals and the specified trial function. In each case, compare the one-term solution to the exact solution. a. day + y = 2x 0<x<1 d.x2 y(O) = 0 y(1) = 0 N.(x) = x(1 - 1) b. dy 0<x<1 dx2 + y = 2 sinx y(O) = 0 y(1) = 0 N. (x) = sin TX c. dy + y2 = 4x 0<x< 1 dx y(0) = 0 y(1) = 0 Ni(x) = x (1 - x) d. dy - y = 2 d.x 0<x< 10 y(O) = 0 y(10) = 0 Ni(x) = x²(10 - x)? e. dy d.x2 dy + y = x 0 <r <1 dx y(O) = 0 y(1) = 0 N. (x) = x(x - 1)? Question 2: For each of the differential equations given in Question 1, use the method of Example 5.4 to determine the trial functions for a two-term approximate solution using Galerkin's method of weighted residuals.
Finite Element Methods HW #8 Problem Specification Determine the nodal displacement, force and stress in each member of the following truss using ANSYS APDL. Indicate if the member is in tension or compression. The cross- sectional area of each member is 8 in2, the Young's modulus is 1.9x106 lb/in2 and Poisson ratio is 0.3. 500 lb 500 lb 3 ft 3 ft (3) (6) un 5 3 ft (2) (4 ) (5) (1) 2