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A 5x5 K matrix, K, the associated external force vector, f and the reaction force vector,...
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force...
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force vector of the Ku f problem using three elements with the lengths prescribed in the figure. Your work should include all boundary conditions. The beam has the properties E 3.0E6 psi and I 4.5 in 30 lb/in Fo-500 q2 20 lb/in 12 in The weak formulation gives the following expressions for the generic element force vector qe and stiffness matrix Ke. 12Eele 6Eel 20...
DKI=3 Problem 1: Determine the following vector and matrix expressions for the frame structure load system show...
DKI=3
Problem 1: Determine the following vector and matrix expressions for the frame structure load system shown below. The vector of unknown displacem ents D; The joint load vector Q; The fixed-end force vector Qo; and The Stiffness matrix K. 1· 2. 3. 4. The vector equation involving the above quantities based on the displacement method is 1-5 K/ft C. 430 24 ft 3 20 ft 20%t 0 0 TiIT
Problem 1: Determine the following vector and matrix expressions for...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the ele...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
(25 pts) 1. Consider the general problem: -( ku '), + cu' + bu = f, 0
(25 pts) 1. Consider the general problem: -( ku '), + cu' + bu = f, 0
QUESTION 2: Consider this forced translational mass-spring-damper (MSD) system: The input is the external force "F(t)"...
QUESTION 2: Consider this forced translational mass-spring-damper (MSD) system: The input is the external force "F(t)" and the output is position "x(t)." The transfer function for this system is g) - 6 - Mz? +BS+K It is known that M - 1 kg. B - 10 mm, and there are three possible values of K: (K = 16 K = 34 NK-89 The only possible external forces "F(t)" have the following Laplace transforms: 1) F,(s) - 0 (corresponding to external...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
2. If the position vector r= 151 - 10j +20k (m) and force F = 250i...
2. If the position vector r= 151 - 10j +20k (m) and force F = 250i + 400 - 600k (N). a) Find the angle between r and F in degrees. 0 = degrees (5 points) b) Calculate vector M = 1=rXF i + j+ k (5 points)
Theory: A vector with nonnegative entries is called a probability vector if the sum of its entries is 1. A square matrix...
Theory: A vector with nonnegative entries is called a probability vector if the sum of its entries is 1. A square matrix is called right stochastic matrix if its rows are probability vectors; a square matrix is called a left stochastic matrix if its columns are probability vectors; and a square matrix is called a doubly stochastic matrix if both the rows and the columns are probability vectors. **Write a MATLAB function function [S1,S2,P]=stochastic(A) which accepts a square matrix A...
Statics 2. If the position vector r= 151 - 10j + 20k (m) and force F...
Statics
2. If the position vector r= 151 - 10j + 20k (m) and force F = 250i + 400 - 600k (N). a) Find the angle between r and F in degrees. 0 = degrees (5 points) b) Calculate vector M=rXF= i + k (5 points)
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force vector of the Ku f problem using three elements with the lengths prescribed in the figure. Your work should include all boundary conditions. The beam has the properties E 3.0E6 psi and I 4.5 in 30 lb/in Fo-500 q2 20 lb/in 12 in The weak formulation gives the following expressions for the generic element force vector qe and stiffness matrix Ke. 12Eele 6Eel 20...
DKI=3
Problem 1: Determine the following vector and matrix expressions for the frame structure load system shown below. The vector of unknown displacem ents D; The joint load vector Q; The fixed-end force vector Qo; and The Stiffness matrix K. 1· 2. 3. 4. The vector equation involving the above quantities based on the displacement method is 1-5 K/ft C. 430 24 ft 3 20 ft 20%t 0 0 TiIT
Problem 1: Determine the following vector and matrix expressions for...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
(25 pts) 1. Consider the general problem: -( ku '), + cu' + bu = f, 0
QUESTION 2: Consider this forced translational mass-spring-damper (MSD) system: The input is the external force "F(t)" and the output is position "x(t)." The transfer function for this system is g) - 6 - Mz? +BS+K It is known that M - 1 kg. B - 10 mm, and there are three possible values of K: (K = 16 K = 34 NK-89 The only possible external forces "F(t)" have the following Laplace transforms: 1) F,(s) - 0 (corresponding to external...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
2. If the position vector r= 151 - 10j +20k (m) and force F = 250i + 400 - 600k (N). a) Find the angle between r and F in degrees. 0 = degrees (5 points) b) Calculate vector M = 1=rXF i + j+ k (5 points)
Statics
2. If the position vector r= 151 - 10j + 20k (m) and force F = 250i + 400 - 600k (N). a) Find the angle between r and F in degrees. 0 = degrees (5 points) b) Calculate vector M=rXF= i + k (5 points)
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