University of Florida - EGM - 5533

University of Florida - EGM - 5533

University of Florida - EGM - 5533

University of Florida - EGM - 5533

EGM 5533 - Period 5Assignment #2ORIGIN 1 MPa 10 Pa6 ORIGIN 106Problem 2.5: 80 20 40 T := 20 60 10 MPa 40 10 20 Stress tensor at a pointa.) Find the stress vector on the plane described by the vector v: 1 v := 2 1n := v v Vector describing a plane

University of Florida - EGM - 5533

University of Florida - EGM - 5533

University of Florida - EGM - 5533

University of Florida - EGM - 5533

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University of Florida - EGM - 5533

University of Florida - EGM - 5533

University of Florida - EML - 4507

0rame2d.mclear all% Added File Managment. Program will request an xls filename from the user% The output is written to an m-file of the input data name suffixed "_out.txt"f_name=input('What is the name of the data file? (*.xls file) ','s');out_name=s

University of Florida - EML - 4507

CIDlowest HW 2nd lowest HWTotal Lowest Qz Quiz Total P116008.510.57.23.018.2916019.513.09.210.517.4 8.516910.00.08.317.719.3 9.516980.00.07.29.518.0 9.518050.00.08.116.019.7 1018950.08.58.83.519.8919420.00.03.81

University of Florida - EML - 4507

CIDHW01 HW02 HW03 HW04 HW05 HW06 HW07 HW08 HW09 HW10 HW11 HW12 Q1Q1N16001910.51113.517.51514.5138.510.5181125 16.7160117191318201915.518.59.519.5172025 16.7169120191217161514.500201815 26.5 17.7169815020618

University of Florida - EML - 4507

EML 4507 Finite Element Analysis & DesignFall 2010HW01Solution3. Consider the following two threedimensional vectors a and b:cfw_1, 4, 6T and bacfw_4, 7, 2T(a) Calculate the scalar product c = a b.(b) Calculate the norm of vector a.(c) Calculate

University of Florida - EML - 4507

EML 4507 Finite Element Analysis & Design0.13.Fall 2010HW02SolutionConsider the matrix equation [A]cfw_x = cfw_b given by2100 x11 x22 x3121404(a) Construct the quadratic form F(x) = cfw_xT[A]cfw_x 2cfw_xTcfw_b.(b) Find cfw_x = cfw_x* by

University of Florida - EML - 4507

EML 4507 Finite Element Analysis & DesignFall 2010HW03Solution12. If the displacement field is given byx2ux2y 2uyy22x (yuzz22xyz)(a) Write down 33 strain matrix.(b) What is the normal strain component in the direction of (1,1,1) at point (

University of Florida - EML - 4507

EML 4507 FEA & DesignFall 2010HW04Solution23. A strain rosette consisting of three strain gages was used to measure the strains at a point in a thin walled plate. The measured strains in the three gages are: A = 0.001, B = 0.0006, and C = 0.0007.Not

University of Florida - EML - 4507

EML 4507 FEA & DesignFall 2010HW05Solution2) Three rigid bodies, 2, 3 and 4, are connected by six springs as shown in the figure. The rigid walls arerepresented by 1 and 5. A horizontal force F3 = 1000 N is applied on Body 3 in the direction shownin

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010HW06Solution18. Use FEM to solve the plane truss shown below. Assume AE = 106 N, L = 1 m. Determine the nodaldisplacements, forces in each element and the support reactions.1yx1L2L2L4310,000 N3Solution:Conn

University of Florida - EML - 4507

EML 4507 FEA & DESGN4Fall 2010HW07Solution2132433142217,656 1125828 x The properties of the members of the truss in the left side of the figure are given in the table.43y6,482 310,000 Calculate the nodal displacement and element

University of Florida - EML - 4507

University of Florida - EML - 4507

EML 4507 FEA & DESGN1. RepeatExample4.2withFall 2010theHW08approximateSolutiondeflectioninthefollowingform:v(x ) = c1x + c2x + c3x . Compare the deflection curve with the exact solution.234Solution:The given form of approximate deflect

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010HW09Solution12. Model the beam shown in the figure using one twonode beam finite element.fL=1m12EI = 0.15 Nm2Lf = 1 N/ma) Using the beam element stiffness matrix, set up the equation for this beam ( [K]cfw_Qcfw_F

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010HW10Solution3. Using two CST elements, solve the simple shear problem described in the figure and determinewhether the CST elements can represent the simple shear condition accurately or not. Materialproperties are given

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010HW11SolutionAn external couple C2 is applied at Node 2 in the beam shown below. When EI = 105 N.m2, therotations in radians at the three nodes are determined to be 1 = 0.025, 2 = +0.05, 3 = 0.025a) Draw the shear force a

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010HW12Solution2. Consider a heat conduction problem described in the figure. Inside of the domain, heat isgenerated from a uniform heat source Qg = 10 W/m3, and the conductivity of the domain is k = 0.1W/m/oC. The cross-se

University of Florida - EML - 4507

Number of nodes= 8Number of elements= 18Node numbers, their coordinates and BCs are: 1 1.00000000 0.00000000 1.00000000 1 1 1 2 1.00000000 1.00000000 1.00000000 1 1 1 3 0.00000000 1.00000000 1.00000000 1 1 1 4 0.00000000 0.00000000 1.00000000 1 1 1

University of Florida - EML - 4507

43001101100110011001101223341.00E+11 1.00E-04 1.00E-091.00E+11 1.00E-04 1.00E-091.00E+11 1.00E-04 1.00E-09010000000000

University of Florida - EML - 4507

EML 4507 FEA & DESGNFall 2010Project 2Due on Monday Dec 6, 2010The aluminum bracket with a central hole is subjected to uniform uniaxial stress as shown. Use Abaqussoftware to determine the deformed shape, and calculate the maximum von Mises stress a

University of Florida - EML - 4507

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 1-1If you want, write your name in the back.SolutionProblem 1: Derive the (cubic) characteristicequation for determining the principalstresses of the stress matrix shown below.Do NOT solve the equation.Since one of the eigen

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 1-2If you want, write your name in the back.SolutionProblem 3: Matrix A given by [A]=8442 and theeigen values of [A] are: 0 and 10.Determine if it is: (a) positive-definite; or (b) Positivesemi definite; or (c) Negative defin

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 1-3If you want, write your name in the back.SolutionProblem 3: Consider a function f(x,y)fx,y=12xy[A]xy-xy40 whereA=9443 . The eigen values of [A] are 1 and 11.It is found that the function is extremum at(x,y)=(0,1). Determi

University of Florida - EML - 4507

University of Florida - EML - 4507

40400.10.10.10.090.080.070.060.050.030.020-0.02-0.03-0.05-0.06-0.07-0.08-0.09-0.1-0.1-0.1-0.1-0.1-0.09-0.08-0.07-0.06-0.05-0.03-0.0200.020.030.050.060.070.080.090.10.100.020.030.050.060.070.080.090.10.10

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 2-v1Solution 1 1 0 0 u1 F1 1 2 1 0 u 1000 5 2 = 10 0 1 3 2 u3 0 0 0 2 2 u4 F4 1000 N1m1m1mA stepped bar is clamped at both ends. A force of1000 N is applied as shown in the figure.Areas of cross sections of the two

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 2-v2Solution 1 1 0 0 u1 F1 1 3 2 0 u 0 5 2 = 10 0 2 4 2 u3 2000 0 0 2 2 u4 F4 2000 N1m1m1mA stepped bar is clamped at both ends. A force of2000 N is applied as shown in the figure.Delete the rows corresponding to u

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 2-v3Solution 1 1 0 0 u1 F1 1 3 2 0 u 0 6 2 = 10 0 2 4 2 u3 +10, 000 0 0 2 2 u4 F4 10 kN1m1m1mA stepped bar is clamped at both ends. A force of10,000 N is applied as shown in the figure.Delete the rows corresponding

University of Florida - EML - 4507

EML 4507 Fall 2010Quiz 5-v1SolutionThe coordinate of the nodes and correspondingdisplacements in a triangular element are givenin the table.1. Calculate the displacements u and v andstrains xx, yy, and xy at the centroid ofthe element given by the

University of Florida - EML - 4507

EML 4507Fall 2010Exam 1-1Write only on the front side. If you want, write yourname in the back. All problems carry equal pointsProblem 1: The state of stress at a point is given by200400[]SolutionProblem 2: The state of stress at a point is giv

University of Florida - EML - 4507

EML 4507Fall 2010Exam 1-2Write only on the front side. If you want, write yourname in the back. All problems carry equal pointsProblem 1: The state of stress at a point is given by400400[]Problem 2: The state of stress at a point is given by:0

University of Florida - EML - 4507

EML 4507Fall 2010Exam1-3Write only on the front side. If you want, write yourname in the back. All problems carry equal pointsProblem 1: The state of stress at a point is given byProblem 2: The state of stress at a point is given by:1000 2 0 MPa0

University of Florida - EML - 4507

tiff1.mfunction [k]=stiff1(L,ll,aa)k1=zeros(2);l=ll(1);m=ll(2);A=aa(1);E=aa(2);k1(1,1)=l*l;k1(1,2)=l*m;k1(2,1)=l*m;k1(2,2)=m*m;k=[k1,-k1;-k1,k1];k=(A*E/L)*k;

University of Florida - EML - 4507

% stiff2.m used with truss3d.mfunction [k]=stiff2(L,ll,aa)k1=zeros(3);l=ll(1);m=ll(2);n=ll(3);A=aa(1);E=aa(2);k1(1,1)=l*l;k1(1,2)=l*m;k1(1,3)=l*n;k1(2,1)=l*m;k1(2,2)=m*m;k1(2,3)=m*n;k1(3,1)=l*n;k1(3,2)=m*n;k1(3,3)=n*n;k=[k1,-k1;-k1,k1];k

University of Florida - EML - 4507

function [k]=stiff2f(L,ll,aa)kb=zeros(6);l=ll(1);m=ll(2);EA=aa(1)*aa(2);EI=aa(1)*aa(3);kb(1,1)=EA/L;kb(1,4)=-kb(1,1);kb(4,4)=kb(1,1);kb(2,2)=EI*12/L^3;kb(2,3)=6*EI/L^2;kb(2,5)=-kb(2,2);kb(2,6)=kb(2,3);kb(3,3)=4*EI/L;kb(3,5)=-kb(2,6);kb(3,6)

University of Florida - EML - 4507

EXAMPLE: CREATING A MODEL OF AN OVERHEAD HOIST WITH ABAQUS/CAEThe instructions for the examples discussed in this manual will focus on using the Model Tree toaccess the functionality of ABAQUS/CAE. Menu bar actions will be considered only when necessary

University of Florida - EML - 4507

User Manual for truss2d.m, Professor B.V. Sankar, University of Florida, GainesvilleThe program truss2d.m reads data from truss2d_data.xls. It also needs the subroutine stiff1.m. Thesethree files should be in one folder. The output is written to the tex

University of Florida - EML - 4507

%truss2d.m reads data from an Excel file called 'truss2d_data.xls'% Worksheets in the xls file have the same name same as the data read clear all% The output is written to the file output.txtfid = fopen('output.m','w');Nodes=xlsread('truss2d_data','N

University of Florida - EML - 4507

3201100-101001012231.00E-04 1.00E+111.00E-04 1.00E+11010000020000

University of Florida - EML - 4507

%truss3d.m reads data from an Excel file called 'truss3d_data.xls'% Worksheets in the xls file have the same name same as the data read clear all% The output is written to the file output.txtfid = fopen('output.m','w');Nodes=xlsread('truss3d_data','N

University of Florida - EML - 4507

8181100110001100110111100001111001111110111111100001234567812341524132341678556783775681.00E-041.00E-041.00E-041.00E-041.00E-041.00E-041.00E-041.00E-041.00E-041

University of Florida - EGM - 6365

Constrained Optimization5Most problems in structural optimization must be formulated as constrained minimization problems. In a typical structural design problem the objective functionis a fairly simple function of the design variables (e.g., weight),

University of Florida - EGM - 6365

Chapter 5: Constrained Optimization5.5 Gradient Projection and Reduced Gradient MethodsRosens gradient projection method is based on projecting the search direction intothe subspace tangent to the active constraints. Let us rst examine the method fort

University of Florida - EGM - 6365

Educational articleStruct Multidisc Optim 21, 120127 Springer-Verlag 2001A 99 line topology optimization code written in MatlabO. SigmundAbstract The paper presents a compact Matlab implementation of a topology optimization code for compliance minimiz

University of Florida - EGM - 6365

University of Florida - EGM - 6365

EGM6365 Homework #21. Consider the following design optimization problem:Minimize2f (x) = x12 + x2 4 x1 + 4Subject tog1 (x) = x1 0g 2 ( x) = x2 0g3 (x) = x2 (1 x1 )3 0(i)(ii)Find the optimum point graphicallyShow that the optimum point does no

University of Florida - EGM - 6365

EGM6365 Homework #31. A linear programming problem is given asMaximizef = 2 x1 + 5 x2Subject to3 x1 + 2 x2 122 x1 + 3x2 6(1)x1 0, x2 unrestricted(i)(ii)Solve Eq. (1) using MATLAB.Convert Eq. (1) into the standard form and solve the standards p

University of Florida - EGM - 6365

EGM6365 Homework#41. Make a Matlab script to solve the following unconstrained optimization problem usinga Newton method.Minimizef ( x) = 1 + 2( x + 1)2 x 3 + e xUse the initial point x = 6 and -6. The iteration should stop when the function gradient

University of Florida - EGM - 6365

EGM6365 Homework #11. A beer can is supposed to hold at least specific amount of beer and meet other designrequirements. The can will be produced in billions, so it is desirable to minimize the costof manufacturing them. Since the cost can be related d

University of Florida - EGM - 6365

EGM6365 Homework #21. Consider the following design optimization problem:Minimize2f (x) = x12 + x2 4 x1 + 4Subject tog1 (x) = x1 0g 2 ( x) = x2 0g3 (x) = x2 (1 x1 )3 0(i)(ii)Find the optimum point graphicallyShow that the optimum point does no

University of Florida - EGM - 6365

EGM6365 Homework #31. A linear programming problem is given asMaximizef = 2 x1 + 5 x2Subject to3 x1 + 2 x2 122 x1 + 3x2 6(1)x1 0, x2 unrestricted(i)(ii)Solve Eq. (1) using MATLAB.Convert Eq. (1) into the standard form and solve the standards p