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(Q2) Write the characteristic matrices of the elements below. (5 marks) E = Young's modulus ofela...
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below...
Finite element method
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below. It is important that the displacement of the slider is accurately known for a given force, F. To find the relation between displacement and F, it was decided to use FE method. Node 1 is fully constrained, node 2 is free to rotate and translate along the horizontal, and node 3 is only free to rotate. (a) Select the appropriate element types for...
A cantilever beam of a channel section is loaded at its half-length, as shown in Figure Q2. The Young's modulus of the material is 200 GPa. Determine the deflection at the free end. [12.5 marks]...
A cantilever beam of a channel section is loaded at its half-length, as shown in Figure Q2. The Young's modulus of the material is 200 GPa. Determine the deflection at the free end. [12.5 marks] 25 mm 25 mm 5 kN a -a 少a 6 mm 200 mm Figure Q2
A cantilever beam of a channel section is loaded at its half-length, as shown in Figure Q2. The Young's modulus of the material is 200 GPa. Determine the deflection at...
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix),...
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), ) Is the state of stress a possible equilibrium stress field? Neglect body forces. 10 point 2. The assemblv shown in
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), )...
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below.
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
The members of the truss shown below have a cross sectional area of 0.0002m^2 and Young's modulus of E=69GPa. De...
The members of the truss shown below have a cross
sectional area of 0.0002m^2 and Young's modulus of E=69GPa.
Determine the deflection at each joint using Finite Element
Method.
500 N 500 N Fuc (compression) Faa (tension) 2 m 500 N 45° 45" ac (compression) Fas (tension)
500 N 500 N Fuc (compression) Faa (tension) 2 m 500 N 45° 45" ac (compression) Fas (tension)
2.3 6/6 points (graded) Brass has a Young's Modulus of E = 97GPa, shear modulus of...
2.3 6/6 points (graded) Brass has a Young's Modulus of E = 97GPa, shear modulus of G = 37GPa and a Poisson's Ratio of v = 0.31. A block of isotropic, linear elastic brass is subjected to an in-plane stress as shown in the figure, where 0, 120MPa, 0y = 110M Pa, Ozy 75 MPa, o, = Ozz = y2 = 0. a) Give numerical values for all strain components. 6 03 Oy os 0 0 ere to search O...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E = 35 x 106 psi. If ui = 0.02 in, and u2 = 0.025 in., considering linear interpolation, determine the following: (a) the displacement at point P; (b) the strain & and stress o; and (c) the element stiffness matrix. u2 2 x = 20 in. x = 15 in. X = 23 in.
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
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...
Finite element method
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below. It is important that the displacement of the slider is accurately known for a given force, F. To find the relation between displacement and F, it was decided to use FE method. Node 1 is fully constrained, node 2 is free to rotate and translate along the horizontal, and node 3 is only free to rotate. (a) Select the appropriate element types for...
A cantilever beam of a channel section is loaded at its half-length, as shown in Figure Q2. The Young's modulus of the material is 200 GPa. Determine the deflection at the free end. [12.5 marks] 25 mm 25 mm 5 kN a -a 少a 6 mm 200 mm Figure Q2
A cantilever beam of a channel section is loaded at its half-length, as shown in Figure Q2. The Young's modulus of the material is 200 GPa. Determine the deflection at...
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), ) Is the state of stress a possible equilibrium stress field? Neglect body forces. 10 point 2. The assemblv shown in
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), )...
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
The members of the truss shown below have a cross
sectional area of 0.0002m^2 and Young's modulus of E=69GPa.
Determine the deflection at each joint using Finite Element
Method.
500 N 500 N Fuc (compression) Faa (tension) 2 m 500 N 45° 45" ac (compression) Fas (tension)
500 N 500 N Fuc (compression) Faa (tension) 2 m 500 N 45° 45" ac (compression) Fas (tension)
2.3 6/6 points (graded) Brass has a Young's Modulus of E = 97GPa, shear modulus of G = 37GPa and a Poisson's Ratio of v = 0.31. A block of isotropic, linear elastic brass is subjected to an in-plane stress as shown in the figure, where 0, 120MPa, 0y = 110M Pa, Ozy 75 MPa, o, = Ozz = y2 = 0. a) Give numerical values for all strain components. 6 03 Oy os 0 0 ere to search O...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E = 35 x 106 psi. If ui = 0.02 in, and u2 = 0.025 in., considering linear interpolation, determine the following: (a) the displacement at point P; (b) the strain & and stress o; and (c) the element stiffness matrix. u2 2 x = 20 in. x = 15 in. X = 23 in.
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
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...
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