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Find the principal values and directions of the second-order tensor T, where the Cartesian components of...
1. Consider the stress tensor T at a particular point in a xyz Cartesian coordinate system....
1. Consider the stress tensor T at a particular point in a xyz Cartesian coordinate system. (30 T = 10 (15 10 15 -35 0 ksi 0 40) The material has a modulus of elasticity equal to 10 psi and a Poisson's ratio of 0.3. The principal stresses are 51, 20, and -37 ksi. (A) Determine the nine elements of the strain tensor € (in/in). (B) Determine the largest principal shear stress (ksi). (C) Determine the Von Mises stress (ksi)....
how can we solve this type problems we dont want specific solution. we want to use...
how can we solve this type problems we dont want specific solution.
we want to use as A input everytime different matrix. three axis
have each rotation degree
symmetric second-order tensor. Such axes are called the principal axes of the tensor. For this case, the basis vectors are actually the unit principal directions l"i". nan, nay. and it can be shown that with respect to principal axes the tensor reduces to the diagonal form Note that the fundamental invariants defined...
Good night. I need help with this problem of continuum mechanics. It is taken from George E. Mase book, "Continuum m...
Good night. I need help with this problem of continuum
mechanics. It is taken from George E. Mase book, "Continuum
mechanics for engineers". The picture has the final answer, but I
don't know the steps to obtain it. Please, explain it step by step.
Thank you so much.
3.28. A certain homogeneous deformation feld results in the finite strain tensor 1 32 Lui = 1 3 1-2 |. Determine the principal strains and their directions for this -22 6 deformation...
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1...
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1 -1 0 2 2 0 01 102 0, find a) The components of the symmetric tensor M(a3) and the antisymme tric tensor ΛΊαβ. b) the components of M and M%
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...
114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expre...
Equation 3.5.10 is below
We were unable to transcribe this image114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expressed as the sum of a tensor and a skew symmetric tensor. We have where the symmetric part is similar to the infinitesimal strain tensor (and a when VuVoul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor 3.i1 We note that there is no restriction placed on the magnitude of Vu...
4 Stress Tensor 1. Given: T=14 1 01 MPa. 0 0 1 (a) find the stress...
4 Stress Tensor 1. Given: T=14 1 01 MPa. 0 0 1 (a) find the stress vector on the plane whose normal is in the direction of +ý (b) Find the normal stress on the same plane. (c) Find the magnitude of the tangential stress on the same plane. (d) Find the three principal directions of stress. Hint: the determinant of a 3 x3 11 a12 13 det a a2 a23a11 (a22033-a3223) a12 a1a33-a31a23)+a13(a2132-a31022) 031 a32 33 Given the following...
1. A velocity field has Cartesian components of: 3t a. Find the magnitude of the acceleration...
1. A velocity field has Cartesian components of: 3t a. Find the magnitude of the acceleration for a fluid particle at point (x.y.z) at time t -(0 b. Will the path of this fluid particle follow the streamline(s)? Explain your answer briefly. (You do not need to calculate these lines!)
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a un...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a unit timelike vector, it is always possible to find a Lorentz transformation such thawill have components (0,0,0,1). Show that if k" is a null vector, i is always possible to find a Lorentz transformation such that k" has components (1,0,0,1). Hence show that if UV,-0, and U"is timelike,...
1. Consider the stress tensor T at a particular point in a xyz Cartesian coordinate system. (30 T = 10 (15 10 15 -35 0 ksi 0 40) The material has a modulus of elasticity equal to 10 psi and a Poisson's ratio of 0.3. The principal stresses are 51, 20, and -37 ksi. (A) Determine the nine elements of the strain tensor € (in/in). (B) Determine the largest principal shear stress (ksi). (C) Determine the Von Mises stress (ksi)....
how can we solve this type problems we dont want specific solution.
we want to use as A input everytime different matrix. three axis
have each rotation degree
symmetric second-order tensor. Such axes are called the principal axes of the tensor. For this case, the basis vectors are actually the unit principal directions l"i". nan, nay. and it can be shown that with respect to principal axes the tensor reduces to the diagonal form Note that the fundamental invariants defined...
Good night. I need help with this problem of continuum
mechanics. It is taken from George E. Mase book, "Continuum
mechanics for engineers". The picture has the final answer, but I
don't know the steps to obtain it. Please, explain it step by step.
Thank you so much.
3.28. A certain homogeneous deformation feld results in the finite strain tensor 1 32 Lui = 1 3 1-2 |. Determine the principal strains and their directions for this -22 6 deformation...
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1 -1 0 2 2 0 01 102 0, find a) The components of the symmetric tensor M(a3) and the antisymme tric tensor ΛΊαβ. b) the components of M and M%
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...
Equation 3.5.10 is below
We were unable to transcribe this image114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expressed as the sum of a tensor and a skew symmetric tensor. We have where the symmetric part is similar to the infinitesimal strain tensor (and a when VuVoul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor 3.i1 We note that there is no restriction placed on the magnitude of Vu...
4 Stress Tensor 1. Given: T=14 1 01 MPa. 0 0 1 (a) find the stress vector on the plane whose normal is in the direction of +ý (b) Find the normal stress on the same plane. (c) Find the magnitude of the tangential stress on the same plane. (d) Find the three principal directions of stress. Hint: the determinant of a 3 x3 11 a12 13 det a a2 a23a11 (a22033-a3223) a12 a1a33-a31a23)+a13(a2132-a31022) 031 a32 33 Given the following...
1. A velocity field has Cartesian components of: 3t a. Find the magnitude of the acceleration for a fluid particle at point (x.y.z) at time t -(0 b. Will the path of this fluid particle follow the streamline(s)? Explain your answer briefly. (You do not need to calculate these lines!)
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a unit timelike vector, it is always possible to find a Lorentz transformation such thawill have components (0,0,0,1). Show that if k" is a null vector, i is always possible to find a Lorentz transformation such that k" has components (1,0,0,1). Hence show that if UV,-0, and U"is timelike,...
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