Derive the element stiffness and force vector for a rod in tension and subjected to a uniform dis...
Derive the element stiffness and force vector for a rod in tension and subjected to a uniform distributed load. This requires your integration of the basis function over the element.
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Derive the element stiffness and force vector for a rod in tension and subjected to a uniform dis...
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force...
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force vector of the Ku f problem using three elements with the lengths prescribed in the figure. Your work should include all boundary conditions. The beam has the properties E 3.0E6 psi and I 4.5 in 30 lb/in Fo-500 q2 20 lb/in 12 in The weak formulation gives the following expressions for the generic element force vector qe and stiffness matrix Ke. 12Eele 6Eel 20...
The coupling rod is subjected to a force of 5 kip. ԵԵԵԵԵ When no load is...
The coupling rod is subjected to a force of 5 kip. ԵԵԵԵԵ When no load is applied the spring is unstretched and d= 10 in. The material is A-36 steel and each bolt has a diameter of 0.25 in. The plates at A, B, and C are rigid and the spring has a stiffness of k=16.1 kip/in. Part A Determine the distance d between C and accounting for the compression of the spring and the deformation of the bolts. Express...
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...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrica...
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrical characteristics of the beam elements are also displayed on the same figure. The frame is subjected to two concentrated loads at nodes 2 and 3 and a uniform distributed load over beam 3. The frame is fixed at nodes 1 and 5. A global coordinate system is established with origin at node 1 and x-y axes positively directed to the right and...
what are the components of the source/force vector in global coordinate system related to the following...
what are the components of the source/force vector in global
coordinate system related to the following frame element subjected
to a uniform distributed load of intensity q0 as shown ?
choose one of the following
2→ 9. © !!! !!!!!!! 3o x N 2 q = [0 ; q0L/2 ; - COL2/12; 0; QOL! 2 ; qOL2/12] q = [qOL/2;0; - COL2/12; qOL/2; 0; COL2/12] q = [q0L/4;qOL(3)0.5/4 ; - qOL2/12 ; q0L/4; COL(3)0.5/4 ; GOL2/12] q = [qOL(3)0.5/4 ;...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is...
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is hinged at A and held in equilibrium by a light cord, as shown in Fig. 9-67. A load W = 22 N hangs from the rod at a distance d so that the tension in the cord is 85 N. (a) Draw a free-body diagram for the rod. (b) Determine the vertical and horizontal forces on the rod exerted by the hinge. (c) Determine...
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...
4. (25 pt.) The beam subjected to a uniform distributed load as shown in Figure 4(a)...
4. (25 pt.) The beam subjected to a uniform distributed load as shown in Figure 4(a) has a triangular cross-section as shown in Figure 4(b). 1) (6 pt.) Determine mathematical descriptions of the shear force function V(x) and the moment function M(x). 2) (6 pt.) Draw the shear and moment diagrams for the beam. 3) (5 pt.) What is the maximum internal moment Mmar in the beam? Where on the beam does it occur? 4) (8 pt.) Determine the absolute...
Given the indeterminate beam shown below, use FEM to compute the final stiffness matrix and force vector of the Ku f problem using three elements with the lengths prescribed in the figure. Your work should include all boundary conditions. The beam has the properties E 3.0E6 psi and I 4.5 in 30 lb/in Fo-500 q2 20 lb/in 12 in The weak formulation gives the following expressions for the generic element force vector qe and stiffness matrix Ke. 12Eele 6Eel 20...
The coupling rod is subjected to a force of 5 kip. ԵԵԵԵԵ When no load is applied the spring is unstretched and d= 10 in. The material is A-36 steel and each bolt has a diameter of 0.25 in. The plates at A, B, and C are rigid and the spring has a stiffness of k=16.1 kip/in. Part A Determine the distance d between C and accounting for the compression of the spring and the deformation of the bolts. Express...
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...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrical characteristics of the beam elements are also displayed on the same figure. The frame is subjected to two concentrated loads at nodes 2 and 3 and a uniform distributed load over beam 3. The frame is fixed at nodes 1 and 5. A global coordinate system is established with origin at node 1 and x-y axes positively directed to the right and...
what are the components of the source/force vector in global
coordinate system related to the following frame element subjected
to a uniform distributed load of intensity q0 as shown ?
choose one of the following
2→ 9. © !!! !!!!!!! 3o x N 2 q = [0 ; q0L/2 ; - COL2/12; 0; QOL! 2 ; qOL2/12] q = [qOL/2;0; - COL2/12; qOL/2; 0; COL2/12] q = [q0L/4;qOL(3)0.5/4 ; - qOL2/12 ; q0L/4; COL(3)0.5/4 ; GOL2/12] q = [qOL(3)0.5/4 ;...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is hinged at A and held in equilibrium by a light cord, as shown in Fig. 9-67. A load W = 22 N hangs from the rod at a distance d so that the tension in the cord is 85 N. (a) Draw a free-body diagram for the rod. (b) Determine the vertical and horizontal forces on the rod exerted by the hinge. (c) Determine...
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...
4. (25 pt.) The beam subjected to a uniform distributed load as shown in Figure 4(a) has a triangular cross-section as shown in Figure 4(b). 1) (6 pt.) Determine mathematical descriptions of the shear force function V(x) and the moment function M(x). 2) (6 pt.) Draw the shear and moment diagrams for the beam. 3) (5 pt.) What is the maximum internal moment Mmar in the beam? Where on the beam does it occur? 4) (8 pt.) Determine the absolute...
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