Part (1): For the simply supported beam and the moment distribution shown in Figure.1, the governing...

Transcribed Image Text:

Part (1): For the simply supported beam and the moment distribution shown in Figure.1, the governing differential equation for the boundary value problem is given by: ΕΙ d²ø dx² - M(x) = 0, Ø(0) = 0 and Ø(9) = 0 EI=1.6(1010) N-cm² hist 1.5 m M(x) 2(10) N-cm 3 m 1.5(10) EI=1.2 (1010) N-cm² 4.5 m EI-2.4(10¹0) N-cm² 3.2(10) Figure. 1: Simply supported beam subjected to moment distribution Critically analyse the finite element product and systems model that help to find and solve the problem shown in Figure. 1 by performing the following steps: f. Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of nodes and elements. g. Construct grid/mesh information table h. Write the shapes function, N, and N, for each element (e) and plot the shape function diagram i. Construct the weight functions for the one-dimensional elements' line/mesh. j. Calculate the nodal deflection values and the distribution through each element using element matrices- Galerkin method. k. Would you increase (refine) the number of nodes/elements for this problem, explain you answer? 1. Justify your mesh/grid divisions for this problem in terms of complication of geometry or materials compositions. m. Estimate the deflection at x = 3.5 as well as the rate of deflection for the corresponding element Part (1): For the simply supported beam and the moment distribution shown in Figure.1, the governing differential equation for the boundary value problem is given by: ΕΙ d²ø dx² - M(x) = 0, Ø(0) = 0 and Ø(9) = 0 EI=1.6(1010) N-cm² hist 1.5 m M(x) 2(10) N-cm 3 m 1.5(10) EI=1.2 (1010) N-cm² 4.5 m EI-2.4(10¹0) N-cm² 3.2(10) Figure. 1: Simply supported beam subjected to moment distribution Critically analyse the finite element product and systems model that help to find and solve the problem shown in Figure. 1 by performing the following steps: f. Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of nodes and elements. g. Construct grid/mesh information table h. Write the shapes function, N, and N, for each element (e) and plot the shape function diagram i. Construct the weight functions for the one-dimensional elements' line/mesh. j. Calculate the nodal deflection values and the distribution through each element using element matrices- Galerkin method. k. Would you increase (refine) the number of nodes/elements for this problem, explain you answer? 1. Justify your mesh/grid divisions for this problem in terms of complication of geometry or materials compositions. m. Estimate the deflection at x = 3.5 as well as the rate of deflection for the corresponding element