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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),...
A cubic block of side lengths h and mass density p rests on a horizontal flat rigid plate, as shown. Assuming that the cube is isotropic and linearly elastic, whose material properties are characteri...
A cubic block of side lengths h and mass density p rests on a horizontal flat rigid plate, as shown. Assuming that the cube is isotropic and linearly elastic, whose material properties are characterized by the Young's modulus (E) and Poisson's ratio (v), determined the strain distribution in the cube due to the gravity field. For what value(s) of the Poisson's ration the cube will not change its lateral dimensions? gravity
A cubic block of side lengths h and mass...
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...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
The displacement field in a steel machine component (Young’s modulus, E = 210 GPa and Poisson’s...
The displacement field in a steel machine component (Young’s modulus, E = 210 GPa and Poisson’s ratio, ? = 0.33) is given (in metres) by the following expressions: ux = c(x2 + ?) + 2c uy = 2cx2 − cy uz = c? + 5c? where c = 10−4. For a point (x, y, z) positioned at (1, 1, 1) calculate a) The strain components; [4 marks] b) The stress components and sketch a stress element showing how they act;...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...
A cubic block of side lengths h and mass density p rests on a horizontal flat rigid plate, as shown. Assuming that the cube is isotropic and linearly elastic, whose material properties are characterized by the Young's modulus (E) and Poisson's ratio (v), determined the strain distribution in the cube due to the gravity field. For what value(s) of the Poisson's ration the cube will not change its lateral dimensions? gravity
A cubic block of side lengths h and mass...
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...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...
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