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3. Write the expressions for the shape functions for a linear truss element. Explain the followin...
2. Shape functions What are they used for? (List at least 3 uses) Explain how to...
2. Shape functions What are they used for? (List at least 3 uses) Explain how to obtain the shape functions for a 1D bar element Explain how to obtain the shape functions for a 2D beam element Explain how to obtain the shape functions for the Q4 element* Differences between a higher and lower order element
2. Shape functions What are they used for? (List at least 3 uses) Explain how to obtain the shape functions for a 1D bar...
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry...
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3 marks) (b) Imman F FIGURE Q2b: 3 Springs (0) Derive an expression for the Total Potential Energy of the structure shown above in Q2b. (5 marks) (1) Apply the minimum potential energy method to derive the...
Linear Systems (3) Write an expression for the following functions using shifted and scaled versions of...
Linear Systems
(3) Write an expression for the following functions using shifted and scaled versions of the unit step function u(t)
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why...
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why it is used (3 marks) What is a shape function? (3 marks) PLEASE TURN OVER 16363,16367 Page 2 of 3 0.2 (a) (Continued) (iii) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3...
Write the MATLAB code and use the function linsolve() to solve the system of linear equations. Thank you! l Truss A truss is a structure that typically consists of 1. All straight members 2. connected...
Write the MATLAB code and use the function linsolve() to solve
the system of linear equations.
Thank you!
l Truss A truss is a structure that typically consists of 1. All straight members 2. connected together with pin joints 3. connected only at the ends of the members 4. and all external forces (loads&reactions) must be applied only at the joints. The weights of the members may be neglected. The basic building block of a truss is a triangle. Large...
3. Properties of an Unspecified Social Welfare Function: You are given a social welfare function that satisfies the independence of irrelevant alternatives and Pareto criteria. There are two indi...
3. Properties of an Unspecified Social Welfare Function: You are given a social welfare function that satisfies the independence of irrelevant alternatives and Pareto criteria. There are two individuals ea and b and three alternatives z, y, and z. When the individual preferences are Individual a: zyr Individual b: x y-z, the social welfare function produces the social ranking a. What can you deduce about the social ranking produced for the following new list of preferences? Individual a:y Individual b:...
Please write functions to decrypt both the shift (Caesar) and linear ciphers. Also, answer the questions...
Please write functions to decrypt both the shift (Caesar) and linear ciphers. Also, answer the questions in Python and show how it typed and ran inside the client. The def is what to start with 1) Write a function called decrypt that accepts three numbers (c, m, and k) and returns the corresponding plaintext (p) value as a number. You can assume the modulus (n) is 256. You will need to compute the multiplicative inverse of m mod 256 to...
Preliminaries For this lab you will be working with regular expressions in Python. Various functions for...
Preliminaries For this lab you will be working with regular expressions in Python. Various functions for working with regular expressions are available in the re module. Fortunately, Python makes it pretty easy to check if a string matches a particular pattern. At the top of the file we must import the re module: import re Then we can use the search() function to test whether a string matches a pattern. In the example below, the regular expression has been saved...
1. True or False, and explain briefly. 1) The assumption that more is better implies that...
1. True or False, and explain briefly. 1) The assumption that more is better implies that the indifference curves are upward sloping 2) Convexity of indifference curves implies that consumers are willing to give up more to get an extra the more they have 3) Consider the following three bundles. Bundle Good Goody If Bundles A and B are on the same indifference curve, preferences satisfy all the usual assumptions introduced in the lecture, Bundle Cis preferred to Bundle A...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...
2. Shape functions What are they used for? (List at least 3 uses) Explain how to obtain the shape functions for a 1D bar element Explain how to obtain the shape functions for a 2D beam element Explain how to obtain the shape functions for the Q4 element* Differences between a higher and lower order element
2. Shape functions What are they used for? (List at least 3 uses) Explain how to obtain the shape functions for a 1D bar...
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3 marks) (b) Imman F FIGURE Q2b: 3 Springs (0) Derive an expression for the Total Potential Energy of the structure shown above in Q2b. (5 marks) (1) Apply the minimum potential energy method to derive the...
Linear Systems
(3) Write an expression for the following functions using shifted and scaled versions of the unit step function u(t)
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why it is used (3 marks) What is a shape function? (3 marks) PLEASE TURN OVER 16363,16367 Page 2 of 3 0.2 (a) (Continued) (iii) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3...
Write the MATLAB code and use the function linsolve() to solve
the system of linear equations.
Thank you!
l Truss A truss is a structure that typically consists of 1. All straight members 2. connected together with pin joints 3. connected only at the ends of the members 4. and all external forces (loads&reactions) must be applied only at the joints. The weights of the members may be neglected. The basic building block of a truss is a triangle. Large...
3. Properties of an Unspecified Social Welfare Function: You are given a social welfare function that satisfies the independence of irrelevant alternatives and Pareto criteria. There are two individuals ea and b and three alternatives z, y, and z. When the individual preferences are Individual a: zyr Individual b: x y-z, the social welfare function produces the social ranking a. What can you deduce about the social ranking produced for the following new list of preferences? Individual a:y Individual b:...
1. True or False, and explain briefly. 1) The assumption that more is better implies that the indifference curves are upward sloping 2) Convexity of indifference curves implies that consumers are willing to give up more to get an extra the more they have 3) Consider the following three bundles. Bundle Good Goody If Bundles A and B are on the same indifference curve, preferences satisfy all the usual assumptions introduced in the lecture, Bundle Cis preferred to Bundle A...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...
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