FIRST PROBLEM ONLY!!!! I\'m a little confused on how to set it up. I doesn\'t sp

Question

FIRST PROBLEM ONLY!!!! I'm a little confused on how to set it up. I doesn't specify(so either one) and I am a little confused on which method to use. Rayleigh Ritz method or Galerkin method to find the weak formulation

EDIT: u = ui*H1(x) + ui+1*H2(x)

H1(x) = xi+1 - x / hi

H2(x) = x - xi / hi

xi+1 and xi are constants

du/dx = ui+1 - ui / hi

du^2/dx^2 = (ui+1)^2 + (ui)^2 +2(ui*ui+1)

A differential equation with boundary conditions is given below dPru du. 3 u(1) 2, and w(4-1 1. Derive the weak formulation 2. Consider four sub intervals then compute the element matrices and vectors using linear shape func- tions 3. Assemble the element matrices and vectors into a global matrix and vector. 4. Apply the boundary conditions to the matrix equations 5. Solve for the unknown nodal points Problem 2 (30 pts) Consider the equilibrium of the rod of negligible weight in Fig.1, where an axial load P 10 N is applied as shown. (E x 109 N/m2) and (A 900 mm are respectively the Young's modulus and cross-sectional area of the rod. The traction (I) varies over the length of the rod according to Eq.1 l. Derive the integral equation of the potential energy (PE) of the rod 2. Using the finite element formulation of the Rayleigh-Ritz method, expand the expression of (PE) using (n 1) sub-intervals between (0 z L 1.0 m). (Assume linear shape functions and a trial solution in the form ui H (z) i I-1 H2(z) between zi and zi 1, where ui represent the displacement at node i). 3. Assemble the element matrices and vectors into a global matrix and global vector then solve for the nodal values. Er A.

Explanation / Answer

Hi, As i searched for the best one and found this one. Please use Rayleigh Ritz's method and your assumption is right.

The derivation looks fine and please sustitute the values accordingly. Feel free to write us for the clarification.

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