# Order Mechanical Engineering Assignment

Order Mechanical Engineering Assignment
Consider a rectangular plate with width W height H , thickness t subject to various in plane
loading and boundary conditions, see Figure 1 to 6. Find the displacement solutions by finite
element method use beam elements. Find the FE solutions by programs in PS-TOOLs-2023.
L=100 CID (in.), H= L/10; E=1e7 psi, t=1 in. We will treat the ‘beam solution’ as the reference
‘exact’ solution. Solve the problem with various meshes and report the best solution in the
answer sheets. Specifically, solve the problem for the following BC and loadings:
(a) Simply-supported, uniformly distributed loading w lb/in along top edge, The load will
produce max deflection of 0.5 in by beam solution. (Total force FT=w*L), see Fighue 1.
(b) Clamped-free BC. Uniformly distributed total force PT applied at the right edge. The load
PT will produce max deflection of 0.5 in by beam solution. See Figure 2.
(c) Clamped-free BC with uniformly distributed loading w lb/in along top edge, The load w
will produce max deflection of 0.5 in by beam solution. (Total force FT=w*L). See Figure
3.
(d) Clamped-supported BC with uniformly distributed loading w lb/in along top edge, The
load w will produce max deflection of 0.5 in by beam solution. (Total force FT=w*L).
See Figure 4.
(e) Clamped-clamped BC with uniformly distributed loading w lb/in along top edge, The
load w will produce max deflection of 0.5 in by beam solution. (Total force FT=w*L).
See Figure 5.
Solve the problem use several meshes and compare the solution with the results obtained by
matlab program dsolve.
Page numbers in solution book:
Problem 1
Part [a] Page ____
Part [b] Page ____
Part [c] Page ____
Part [d] Page ____
Part [e] Page ____
Remarks: ignore the dimemsion tic in the above figure.
Order Mechanical Engineering Assignment
Problem 2(20%): Convergence of Plane stress analysis of 2-D Plate
models For the model of Figure 4, use the following data W=100 CID (in.), H=W; E=1e7 psi, t=1 in. Find
converged maximum deflection and max stress by finite element method, use programs in PS-
TOOLs-2023. That is, solve the problem use various meshes until the maximum responses is
within 2 percent.
Page numbers in solution book:
Problem 2 : Page________
Problem 3(20%): Long hand plane stress analysis of an L-plate Consider the L-plate shown in Figure 7 defined by points A to F . The edge AF is clamped with
uniformly distributed vertical load 50 lb/in along C to D. Solve the plane stress problem by finite
element method use Matlab-aided longhand solution.
Geometrical Data for the L-Plate: L=40 in., t=1 in =thickness
AF=W1 =L CID, BC=2*L, AB=2*L, FE=AF. (ignore the coordinate tics in the figures)
Material properties: E=1e7 psi, v=0.3.
Use the following 4 element FE mesh:
One R8 element for domain APEF
One R4 element for domain BPQE
Two T3 elements for domain EQCD
Where P is the intersection point of the extension of DE and line AB;
and Q is the intersection point of the extension of FE and line BC;
Page numbers in solution book:
Problem 3 : Page________
Problem 4 (10%) High order beam elements
Solve all cases of Problem 1, use 1 Beam6A element.

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