spring element (finite element analysis)
Find the stiffness matrices for each element and the large (general) set of equations of the system.
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FEA ( finite element analysis ) c) In terms of performing a finite element analysis, describe...
FEA
( finite element analysis )
c) In terms of performing a finite element analysis, describe the phrase "stress miffening, Inverse of buckling Increase in transverse stiffness wol increase of axial force d) Describe geometric nonlinearities and when they should be used.
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [M...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
Finite Element Analysis CVE705 Stiffness Matrix Problem: An eight-node element assemblage shown is used in a...
Finite Element Analysis
CVE705
Stiffness Matrix
Problem:
An eight-node element assemblage shown is used in a finite
element analysis.
Calculate the diagonal element of the stiffness matrix
corresponding to the degree of freedom U100
shown.
Use a plane stress case
E = 10,000
v = 0.3
t = 1.0
U100
Determine the finite element model (i.e., the equations of motion) for a free-free bar with the f...
Determine the finite element model (i.e., the equations of motion) for a free-free bar with the following 3 node, 2 bar element mesh (30pts): 5) U(t) E,ρ 0 L/3 The element stiffiness and mass matrices for a bar element of length L are: EAI 1-1 L L-1 1 6 1 2
Determine the finite element model (i.e., the equations of motion) for a free-free bar with the following 3 node, 2 bar element mesh (30pts): 5) U(t) E,ρ 0 L/3...
Question 1 a) What are the steps involved in Finite element analysis? b) Attempt to formulate...
Question 1 a) What are the steps involved in Finite element analysis? b) Attempt to formulate a mathematical model of a steel electric distribution pole.Write the Matlab code for solving the problem. c) Carefully study the spring system shown below. Solve the problem using direct stiffness method. ko FC - 4, 4540 Ribar
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is...
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is sine cose 0 0 0 0 0 sine 0 0 0 -sine cose 0 0 In the previous section, we developed the stines matributed to bending for a beancement. This matracounts for lateral deplacements and rotaties teach mode andis TO 0 0 0 60-126 0 0 0 0 0 LO 621041 To represent the contribution of each term to nodal degrees of freedom, the...
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...
Problem3 The following problem is intended to be solved by hand. For the structure shown below A.) Label the structure degrees of freedom (free only) and number the elements B.) For each element, det...
Problem3 The following problem is intended to be solved by hand. For the structure shown below A.) Label the structure degrees of freedom (free only) and number the elements B.) For each element, determine the stiffness matrix in global element coordinates. Label each row and column of each element matrix with its corresponding global DoF. C.) Assemble the structure stiffness matrix Kfr from the element global stiffness matrices D.) Calculate the deflection of the free DoFs. 5 ft 500 k...
5 Node Element i k (2) (1) (3) 1 4 3 2 2 5 5 2...
5 Node Element i k (2) (1) (3) 1 4 3 2 2 5 5 2 (1) (2) (3) 2 3 7.2 The stiffness matrices and force vectors of the three two-dimensional thermal elements given in Fig. 7.5 are as follows. Assemble the terms to produce the system equations. [5 211 6 31 [k(1)] = [k(*)] = 2 10 2 [(2)] = 3 12 4 1 26 1 46 {f}} = {3} 20 24 24 16 10 16
FEA
( finite element analysis )
c) In terms of performing a finite element analysis, describe the phrase "stress miffening, Inverse of buckling Increase in transverse stiffness wol increase of axial force d) Describe geometric nonlinearities and when they should be used.
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
Finite Element Analysis
CVE705
Stiffness Matrix
Problem:
An eight-node element assemblage shown is used in a finite
element analysis.
Calculate the diagonal element of the stiffness matrix
corresponding to the degree of freedom U100
shown.
Use a plane stress case
E = 10,000
v = 0.3
t = 1.0
U100
Determine the finite element model (i.e., the equations of motion) for a free-free bar with the following 3 node, 2 bar element mesh (30pts): 5) U(t) E,ρ 0 L/3 The element stiffiness and mass matrices for a bar element of length L are: EAI 1-1 L L-1 1 6 1 2
Determine the finite element model (i.e., the equations of motion) for a free-free bar with the following 3 node, 2 bar element mesh (30pts): 5) U(t) E,ρ 0 L/3...
Question 1 a) What are the steps involved in Finite element analysis? b) Attempt to formulate a mathematical model of a steel electric distribution pole.Write the Matlab code for solving the problem. c) Carefully study the spring system shown below. Solve the problem using direct stiffness method. ko FC - 4, 4540 Ribar
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is sine cose 0 0 0 0 0 sine 0 0 0 -sine cose 0 0 In the previous section, we developed the stines matributed to bending for a beancement. This matracounts for lateral deplacements and rotaties teach mode andis TO 0 0 0 60-126 0 0 0 0 0 LO 621041 To represent the contribution of each term to nodal degrees of freedom, the...
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...
Problem3 The following problem is intended to be solved by hand. For the structure shown below A.) Label the structure degrees of freedom (free only) and number the elements B.) For each element, determine the stiffness matrix in global element coordinates. Label each row and column of each element matrix with its corresponding global DoF. C.) Assemble the structure stiffness matrix Kfr from the element global stiffness matrices D.) Calculate the deflection of the free DoFs. 5 ft 500 k...
5 Node Element i k (2) (1) (3) 1 4 3 2 2 5 5 2 (1) (2) (3) 2 3 7.2 The stiffness matrices and force vectors of the three two-dimensional thermal elements given in Fig. 7.5 are as follows. Assemble the terms to produce the system equations. [5 211 6 31 [k(1)] = [k(*)] = 2 10 2 [(2)] = 3 12 4 1 26 1 46 {f}} = {3} 20 24 24 16 10 16
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