Derive stiffness matrix using Galerkin's method:Using Galerkin's method, derive the stiffness matrix for the following beam element, which has an additional node in the center (higher-order element). Let the displacements be v(x) = a1x a2 a3x^3 a4x^2 a5x a6 (two degrees of freedom per node).132-L/20L/2
Derive stiffness matrix using Galerkin's method:Using Galerkin's method, derive the stiffness matrix for the following beam element, which has an additional node in the center
VIDEO ANSWER: We are considering the system from here somewhat like this. Let's say it is plain 1 from here. Let's say this is 2, this from here, let's say 3 s…
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Discontinuous Galerkin Finite Elements for the Einstein Equations - Canadian Institute for Theoretical Astrophysics
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SOLVED: Text: Finite Element MethodsQuestion 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. dy/dx y = 2sin(x), 0 < x < 1, y(0) = 0, y(1) = 0b. dy/dx y = sin(x), 0 < x < T, y(0) = 0, y(T) = 0c. p(x)dy/dx y = 4x, 0 < x < 1, y(0) = 0, y(1) = 0d. p(x)dy/dx - y = 2, 0 < x < 1, y(0) = 0
SOLVED: Text: Finite Element MethodsQuestion 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. dy/dx y = 2sin(x), 0 < x < 1, y(0) = 0, y(1) = 0b. dy/dx y = sin(x), 0 < x < T, y(0) = 0, y(T) = 0c. p(x)dy/dx y = 4x, 0 < x < 1, y(0) = 0, y(1) = 0d. p(x)dy/dx - y = 2, 0 < x < 1, y(0) = 0
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