El = 2.5(1010) N.cm?El = 1.5(1010) N.cm?El = 1.3(1010) N.cm?6m4m2m2.5(10°)2.5(10°)1.5(10°)Figure. 1: Simply supported beam subjected to moment distributionCritically analyse the finite element product and systems model that help to find and solve the problem shown inFigure.1 by performing the following steps:Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling ofnodes and elements.b. Construct grid/mesh information tablec.. Write the shapes function, N; and N; for each element (e) and plot the shape function diagramа.d. Construct the weight functions for the one-dimensional elements' line/mesh.Calculate the nodal deflection values and the distribution through each element using element matrices-е.Galerkin's method.f. Would you increase (refine) the number of nodes/elements for this problem, explain you answer?g. Justify your mesh/grid divisions for this problem in terms of complication of geometry or materialscompositions.h. Estimate the deflection at x = 8.0 as well as the rate of deflection for the corresponding elementM(x) N.cm Problem 3: For the simply supported beam and the moment distribution shown in Figure.1, the governingdifferential equation for the boundary value problem is given by:d2ØEI -M(x) = 0, Ø(0) = 0 and Ø(12) = 0-dx?

Given That As this is Simply Supported Beam We are using method of Finite element Method ***As per…

a. Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of nodes and elements. b. Construct grid/mesh information table c. Write the shapes function, N; and N; for each element (e) and plot the shape function diagram

a. Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of nodes and elements. b. Construct grid/mesh information table c. Write the shapes function, N; and N; for each element (e) and plot the shape function diagram

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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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

El = 2.5(1010) N.cm?
El = 1.5(1010) N.cm?
El = 1.3(1010) N.cm?
6m
4m
2m
2.5(10°)
2.5(10°)
1.5(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:
Construct one-dimensional elements line (i.e., grid/mesh line), make the correct numbering and labeling of
nodes and elements.
b. Construct grid/mesh information table
c.. Write the shapes function, N; and N; for each element (e) and plot the shape function diagram
а.
d. Construct the weight functions for the one-dimensional elements' line/mesh.
Calculate the nodal deflection values and the distribution through each element using element matrices-
е.
Galerkin's method.
f. Would you increase (refine) the number of nodes/elements for this problem, explain you answer?
g. Justify your mesh/grid divisions for this problem in terms of complication of geometry or materials
compositions.
h. Estimate the deflection at x = 8.0 as well as the rate of deflection for the corresponding element
M(x) N.cm

Problem 3: 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:
d2Ø
EI -
M(x) = 0, Ø(0) = 0 and Ø(12) = 0
-
dx?

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