![A) Total potential energy of a spring system Write the expression for the total potential energy of the spring system below 11 ki 43 1lg ii) Specify the boundary conditions B) Shape function and its properties i) Write the expression for the shape function matrix N- [N(C) N,(o)] and strain- !-[ dN displacement matrix B=|ー1 for a typical two-node linear trusbar element shown dx below N, (x) = N, (x) x,-x, x2-XI x1 Element 1 Node 2 Node 1 ii) What is the value of N,倆), Ni(xj), N,(4), N2(x), N(x) +N2(x), and N,(x)x, + N2(x), ?](http://img.homeworklib.com/questions/c232bd60-9b79-11eb-932e-1fc0a2a84836.png?x-oss-process=image/resize,w_560)
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Finite element method
A) Total potential energy of a spring system Write the expression for the...
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...
Problem 2. Consider a finite element with shape functions N1 (ξ) and N2Ģ) used to interpolate...
Problem 2. Consider a finite element with shape functions N1 (ξ) and N2Ģ) used to interpolate the displacement field within the element shown below. Derive an expression for the strain-displacement matrix B where strain E-Bq, in terms of N1 and N2. (Do not assume any specific form for N and N2.) (Note: q[1 21.) 72--
3.4. Consider a finite element with shape functions N(E) and N2(E) used to interpolate the displacement...
3.4. Consider a finite element with shape functions N(E) and N2(E) used to interpolate the displacement field within the element (Fig. P3.4) 2 1 9-> 92-> +1 6-1 FIGURE P3.4 Derive an expression for the strain-displacement matrix B, where strain e Bq, in terms of N and N. (Do not assume any specific form for N or N.) (Note: qa )
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...
PLEASE WRITE/PRINT CLEARLY AND SOLVE USING THE FINITE ELEMENT METHOD UNCLUDING MATRICIES 2. The flow rate...
PLEASE WRITE/PRINT CLEARLY AND SOLVE USING THE FINITE ELEMENT
METHOD UNCLUDING MATRICIES
2. The flow rate at node 1 is 0.16 liter/s (0.16 *10-2 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L=10 m D=20 mm u = 8 x...
PLEASE WRITE/PRINT CLEARLY PLEASE SOLVE USING THE FINITE ELEMENT METHOD WHICH INCLUDES THE MATRIXES 2. The...
PLEASE WRITE/PRINT CLEARLY PLEASE SOLVE USING THE FINITE ELEMENT
METHOD WHICH INCLUDES THE MATRIXES
2. The flow rate at node 1 is 0.16 liter/s (0.16 *10 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L= 10 m D-20 mm [2]...
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...
At the spring meeting of the American Potential Energy Society, a debate erupts over the choice...
At the spring meeting of the American Potential Energy Society, a debate erupts over the choice of a reference point for elastic potential energy. One faction (group #1) feels it is only natural to choose the reference point at the location at which the spring is neither stretched nor compressed and to measure the elastic potential energy relative to that unstrained configuration. Another faction (group #2), whose members always like to think "outside of the box", wants to choose the...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ;...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ; -a sxs a zone II U, > 0 (+ve) 10 ; x> a We consider zone III E>0: Unbound or scattering states (a) State the Time independent Schrödinger's Equation (TISE) and the expression of wave number k in each zone for the case of unbound state (b) Determine the expression of wave function u in each zone. (e) Determine the expression of probability Density...
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...
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...
Problem 2. Consider a finite element with shape functions N1 (ξ) and N2Ģ) used to interpolate the displacement field within the element shown below. Derive an expression for the strain-displacement matrix B where strain E-Bq, in terms of N1 and N2. (Do not assume any specific form for N and N2.) (Note: q[1 21.) 72--
3.4. Consider a finite element with shape functions N(E) and N2(E) used to interpolate the displacement field within the element (Fig. P3.4) 2 1 9-> 92-> +1 6-1 FIGURE P3.4 Derive an expression for the strain-displacement matrix B, where strain e Bq, in terms of N and N. (Do not assume any specific form for N or N.) (Note: qa )
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...
PLEASE WRITE/PRINT CLEARLY AND SOLVE USING THE FINITE ELEMENT
METHOD UNCLUDING MATRICIES
2. The flow rate at node 1 is 0.16 liter/s (0.16 *10-2 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L=10 m D=20 mm u = 8 x...
PLEASE WRITE/PRINT CLEARLY PLEASE SOLVE USING THE FINITE ELEMENT
METHOD WHICH INCLUDES THE MATRIXES
2. The flow rate at node 1 is 0.16 liter/s (0.16 *10 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L= 10 m D-20 mm [2]...
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...
At the spring meeting of the American Potential Energy Society, a debate erupts over the choice of a reference point for elastic potential energy. One faction (group #1) feels it is only natural to choose the reference point at the location at which the spring is neither stretched nor compressed and to measure the elastic potential energy relative to that unstrained configuration. Another faction (group #2), whose members always like to think "outside of the box", wants to choose the...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ; -a sxs a zone II U, > 0 (+ve) 10 ; x> a We consider zone III E>0: Unbound or scattering states (a) State the Time independent Schrödinger's Equation (TISE) and the expression of wave number k in each zone for the case of unbound state (b) Determine the expression of wave function u in each zone. (e) Determine the expression of probability Density...
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...
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