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Determine the finite element model (i.e., the equations of motion) for a free-free bar with the f...
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculatio...
finite element method
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculation question Consider axial vibration of the circular steel bar shown in Figure 4. The steel bar properties are: p- 7800 kg/m and E-200 GPa. (a)lf the first two natural frequencies are required, sketch the finite element model with clearly labelled element numbers and node numbers, State the element types and the degree of freedoms solved (5 Marks (b)Calculate the stiffiness and...
Element 1 is a steel bar that has a circular cross-section with a radius of 30...
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
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...
Problem 3. (3 points). Determine the nodal displacements and reaction forces using the finite element direct...
Problem 3. (3 points). 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 m. Element 2 has Young's Modulus of 200...
need to solve the mathematical model to prove that we can get the equations i Q1...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
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...
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...
For the rod loaded axially as shown in the Figure, determine the axial displacement of the free end. Let E-30x 10s psi, A 2 in2, and L 60 in. Use the finite element stiffhess method. For...
For the rod loaded axially as shown in the Figure, determine the axial displacement of the free end. Let E-30x 10s psi, A 2 in2, and L 60 in. Use the finite element stiffhess method.
For the rod loaded axially as shown in the Figure, determine the axial displacement of the free end. Let E-30x 10s psi, A 2 in2, and L 60 in. Use the finite element stiffhess method.
Problem 4. (3 points). Determine the nodal displacements and reaction forces using the finite ele...
Problem 4. (3 points). 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 bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed Elements 1, 2 and 3 have Young's Modulus of Ei-300 Pa, E2-200 Pa, Es-200 Pa. All elements have o ae of 20 N 20 N...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
finite element method
.'ו Optus 11:56 AM Expert Q&A Finite element method QUESTION 4(20 Marks) - concept and calculation question Consider axial vibration of the circular steel bar shown in Figure 4. The steel bar properties are: p- 7800 kg/m and E-200 GPa. (a)lf the first two natural frequencies are required, sketch the finite element model with clearly labelled element numbers and node numbers, State the element types and the degree of freedoms solved (5 Marks (b)Calculate the stiffiness and...
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
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...
Problem 3. (3 points). 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 m. Element 2 has Young's Modulus of 200...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
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...
For the rod loaded axially as shown in the Figure, determine the axial displacement of the free end. Let E-30x 10s psi, A 2 in2, and L 60 in. Use the finite element stiffhess method.
For the rod loaded axially as shown in the Figure, determine the axial displacement of the free end. Let E-30x 10s psi, A 2 in2, and L 60 in. Use the finite element stiffhess method.
Problem 4. (3 points). 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 bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed Elements 1, 2 and 3 have Young's Modulus of Ei-300 Pa, E2-200 Pa, Es-200 Pa. All elements have o ae of 20 N 20 N...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
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