Engineering - Mechanical Engineering Assignment Related to finite element analysis

AE 5310 Spring 2023

Final Exam Part 1(80) ,

Due 12:30 May 2, 2023

Name_______________ CID___________

Student ID_________________

1. Open books and notes

2. Work independently

3. Submit a solution book with all hand

calculations, if any, and PS tool input

files. Include the problem statements in

the solution book.

4. Submit your solution book on May 2with the

following options [i] turn in a hard copy

[ii] upload a soft copy .

Problem 1 (40%): Convergence FE solution of beam models

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.

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.

Problem 5 (10%) High order beam elements

Solve all cases of Problem 1, use 1 Beam6B element.