FEA Problem 3•Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of theequationddu(1+x)·= 0 for 0 < x < 1dxdxu (0)=0, u(1) = 1Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute theRitz coefficients.

Concept Explanation: Ritz Approximation Method:-The given problem requires solving a boundary value…

Answered: Problem 3 • Compute the coefficient…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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INSTRUCTIONS: Solve the following problem by manually applying the finite element method, following these steps: Pre-processing: Geometry identification. Material properties identification. Load identification. Boundary condition identification. Development of the connectivity matrix for nodes and elements. Processing: Calculation of local stiffness matrices. Assembly of the global stiffness matrix. Assembly of the global force matrix (if required). Application of boundary conditions. Resolution of the system of equations. Derivation of the complete displacement vector (u). Post-processing: Reaction forces calculation. Stress analysis. Problem Statement: the truss nodes and elements (in parentheses) are already numbered. The areas (are in cm^2 ) are underlined. members are made of structural steel, modulus of elasticity is (E) of 20×10^6 N/cm^2 . the lengths are given in cm.
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アN 0. 2. B=2 Matrix ) Find all the eigen values. ) Calculate the eigenvector correspon ding to the Caleulare largest eigenvalue.
Q1 Use Matlab to find the roots of the following polynomials: (a) P₁ = 2s5 — 4s² + 3s³ − 2s² + 3s + 5 (b) P2 =S s6 + 5s³ s² + 10 -
3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0
Solve 4.9 row a USING THE ANALYTICAL METHOD
Given the data below: Xo = 1 X1= 2 x2 = 4 Axo) = 2 Ax1) = 3 Ax2 : = 8 (i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating polynomial. (ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3, i.e., (3). (iii)Calculate the percentage relative error if the true value of f(3) is 4.8.
3. Use Variation of Parameters to solve: y" - 5y +6y= cosh² t, y(0) = 1, y'(0) = 0
3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0
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(b) A beam is subjected to a linearly increasing distributed load. The elastic curve (deflection) is shown in the figure. The equation to find the maximum deflection is given below. Create a matlab code where you can calculate the maximum deflection (dy/dx=0) using the bisection method. Use initial guesses of 1 and 4, L= 6.46 m, E = 59000 kN/cm2, I=35000 cm4, and w0= 2.5 kN/cm. What will be the value of x (location of maximum deflection) after 14 bisection iteration? wo -23 +2L?x³ – L^x) 120EIL dy wo (-5x4 + 6L²a² – Lª) da 120EIL Choices 1.4445 O 2.6001 O4.3335 O 2.889
3. Use the second method of frame assignment, and find the Jacobian of the following robot using the velocity propagation method (Ignore all theta related offsets): 03 02 L2 01 Please answer the question precisely and completely to use the second method of frame assignment to find the D-H table [alpha (i-1) , a (i-1) , d (i) , theta (i)], and find the jacobian matrix using the velocity propagation method

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