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For an isotropic material, (a) Calculate the components of the strain tensor and the stress tensor...
1). It is found that the displacements in a component are described by x} + v(x*...
1). It is found that the displacements in a component are described by x} + v(x* – x3) VX, X2 XX3 u, (x), X2, X3) u, (x7, X2,x;) uz(X, X2, X3) = 2a where a and v are constants. Determine the strain components in the component. = a a 2). The strain tensor at a material point in a steel component is obtained from an FEA as -180 -242 0 E = -242 -3500 x 10-6 0 0 0 Assuming...
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), )...
6. Let the components of the Cauchy stress tensor for an object B at time t...
6. Let the components of the Cauchy stress tensor for an object B at time t be 0 CX3 T = [Tj] = | bx3 ax2 cx1 MPa, where b, c, and d are constants . - 0 -bx10 (a) Determine the body forces required if the object B is at rest for all times t. (b) At the location x - (4,7,-4), calculate the traction vector acting on the surface defined by -X1 + 2x2 + 2x3-2-0 and the...
2. In the absence of body forces, do the following stress components satisfy the equations of...
2. In the absence of body forces, do the following stress components satisfy the equations of equilibrium? 011 = a [až +v (zł – za)], 022 = a [xí +v (zá – z)] , 033 1,033 = av (2ỉ + x3) -2av2122,013 = 031 = 0,023 = 032 = 0 012 = 021 =
σ(MPa) 400 The stress-strain diagram for a ductile material is shown at right. Determine approximately the...
σ(MPa) 400 The stress-strain diagram for a ductile material is shown at right. Determine approximately the modulus of elasticity E. 300 nd the yield stress σγ using the 0.2% offset strain method. If the shear modulus is known to be G 48GPa, compute 200- Poisson's ratio v. The test specimen for this material shown below is stretched with a force P 24kN. Find the resulting 100 hanges in dimensions of the specimen. 10 mm 0.004 0.008 0016 0 100 mm...
3). The stress tensor at a critical point of a structure from an FEA is (120...
3). The stress tensor at a critical point of a structure from an FEA is (120 0 0 0 = 0 -500 0 MPa 0 0 -300 What is the maximum shear stress value at that point? Assume that the structure is made from a brittle grey cast iron. Experimental tests found that the tensile strength for the material is 152 MPa and the compressive strength is 572 MPa. Applying Mohr's criterion for brittle materials, will the structure be safe?...
Subject Composite Materials Please Derive σ22 and σ12 ( Please refer picture). There was an examp...
Subject Composite Materials
Please Derive σ22 and σ12 ( Please refer picture). There was an
example of σ11. Based on the reference.
Please solve σ22 & σ12.
Stress-Strain Relations for Arbitrary Orientation of a Lamina Stress Transformation We use tesors transfer stresses between the two coordinate syslems a) Transformation of coordin P(x,y x1 -Material coordinate system x-y Reference coordinate system Example: i-1 Consider a point P(x,y), its coordinates in x x2 system is P(x,y) Similarly we can establish the other...
Q1. [15 Marks] The stress field in a thin flat structural member can be described by...
Q1. [15 Marks] The stress field in a thin flat structural member can be described by the following equations: Ox 20x + 30xy2 + 20y Oy = 30x2 – 50xy + 20 Txy = 20x – 100y? 02 = Txz = Tyz = 0 where (x, y, z) are in metres and the stress components are in MPa. a) Determine the body forces required to support the structural member in equilibrium; [2 marks] b) Draw a 2D stress element at...
The figure on the left below shows a stress block (plane strain condition is assumed, z...
The figure on the left below shows a stress block (plane strain condition is assumed, z axis is not shown here). Its components as well as the material properties are, • 0,= 10 MPa . O, is currently unknown • Txy = 30 MPa • Young's Modulus E = 150 GPa • Poisson's Ratio V=-0.25 • Note: Poisson's Ratio is negative Rotate the x-y axes in the anticlockwise direction by 45° (as shown in the figure on the right below),...
1). It is found that the displacements in a component are described by x} + v(x* – x3) VX, X2 XX3 u, (x), X2, X3) u, (x7, X2,x;) uz(X, X2, X3) = 2a where a and v are constants. Determine the strain components in the component. = a a 2). The strain tensor at a material point in a steel component is obtained from an FEA as -180 -242 0 E = -242 -3500 x 10-6 0 0 0 Assuming...
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), )...
6. Let the components of the Cauchy stress tensor for an object B at time t be 0 CX3 T = [Tj] = | bx3 ax2 cx1 MPa, where b, c, and d are constants . - 0 -bx10 (a) Determine the body forces required if the object B is at rest for all times t. (b) At the location x - (4,7,-4), calculate the traction vector acting on the surface defined by -X1 + 2x2 + 2x3-2-0 and the...
2. In the absence of body forces, do the following stress components satisfy the equations of equilibrium? 011 = a [až +v (zł – za)], 022 = a [xí +v (zá – z)] , 033 1,033 = av (2ỉ + x3) -2av2122,013 = 031 = 0,023 = 032 = 0 012 = 021 =
σ(MPa) 400 The stress-strain diagram for a ductile material is shown at right. Determine approximately the modulus of elasticity E. 300 nd the yield stress σγ using the 0.2% offset strain method. If the shear modulus is known to be G 48GPa, compute 200- Poisson's ratio v. The test specimen for this material shown below is stretched with a force P 24kN. Find the resulting 100 hanges in dimensions of the specimen. 10 mm 0.004 0.008 0016 0 100 mm...
3). The stress tensor at a critical point of a structure from an FEA is (120 0 0 0 = 0 -500 0 MPa 0 0 -300 What is the maximum shear stress value at that point? Assume that the structure is made from a brittle grey cast iron. Experimental tests found that the tensile strength for the material is 152 MPa and the compressive strength is 572 MPa. Applying Mohr's criterion for brittle materials, will the structure be safe?...
Subject Composite Materials
Please Derive σ22 and σ12 ( Please refer picture). There was an
example of σ11. Based on the reference.
Please solve σ22 & σ12.
Stress-Strain Relations for Arbitrary Orientation of a Lamina Stress Transformation We use tesors transfer stresses between the two coordinate syslems a) Transformation of coordin P(x,y x1 -Material coordinate system x-y Reference coordinate system Example: i-1 Consider a point P(x,y), its coordinates in x x2 system is P(x,y) Similarly we can establish the other...
Q1. [15 Marks] The stress field in a thin flat structural member can be described by the following equations: Ox 20x + 30xy2 + 20y Oy = 30x2 – 50xy + 20 Txy = 20x – 100y? 02 = Txz = Tyz = 0 where (x, y, z) are in metres and the stress components are in MPa. a) Determine the body forces required to support the structural member in equilibrium; [2 marks] b) Draw a 2D stress element at...
The figure on the left below shows a stress block (plane strain condition is assumed, z axis is not shown here). Its components as well as the material properties are, • 0,= 10 MPa . O, is currently unknown • Txy = 30 MPa • Young's Modulus E = 150 GPa • Poisson's Ratio V=-0.25 • Note: Poisson's Ratio is negative Rotate the x-y axes in the anticlockwise direction by 45° (as shown in the figure on the right below),...
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