3- Consider a thin elastic plane of thickness t with a given in-plane displacement of ſu(x,...
3. Consider a thin elastic plane of thickness t with a given in-plane displacement of ſu(x,y) = $dz 5)2 + +d22 (v(x,y) = {2,5)2 +d2 (1) a) Find an expression for all the strain components on this plane. (10 points) b) Find an expression for all the stress components on this plane. (10 points) c) Write down the integral equation to calculate the force on edge A of this plane. (you do not need to solve the integral). (5 points)...
3. Consider a thin elastic plane of thickness t with a given in-plane displacement of ſu(x,y) = $dz 5)2 + +d22 (v(x,y) = {2,5)2 +d2 (1) a) Find an expression for all the strain components on this plane. (10 points) b) Find an expression for all the stress components on this plane. (10 points) c) Write down the integral equation to calculate the force on edge A of this plane. (you do not need to solve the integral). (5 points)...
3- Consider a thin elastic plane of thickness t with a given in-plane displacement of (u(x, y) =şd,67)+ d2m2 |u(x,y) = d763)2 +d263 a) Find an expression for all the strain components on this plane. (10 points) b) Find an expression for all the stress components on this plane. (10 points) c) Write down the integral equation to calculate the force on edge A of this plane. (you do not need to solve the integral). (5 points) d) Write down...
62 (1%) Consider a rectangular plate with sides a and b and thickness t, as shown in the figure at left below. a. Biharmonic equation. If we assume an Airy's stress function: Ф(x,y)-p(x'-y'), where p is a constant, will the biharmonic equation be satisfied? Ignore the body forces. b. Stresses. Determine the stresses (σ.σ..). c. Resultant forces & moment. Apply the Saint-Venant's Principle to find the resultant normal and shearing boundary forces as well as resuitant bending moment along all...
Consider a rectangular plate with sides a and b and thickness t, as shown in the figure at left below. a. Resultant forces & moment, Apply the Saint-Venant's Principle to find the resultant normal and shearing boundary forces as well as resultant bending moment along the left (x-0,0sysb) and right (x-a0sysb) edges of the plate. The respective sense of each resultant is defined in the figure at right below. b Plane stress vs plane strain. The solutions to the above...
For a plane strain extrusion process shown in the figure, the knowns are: the initial and final thickness of the workpiece t0 and t1, (the width w is much larger than the thickness), the wedged die semi angle α, the deformation zone is from section a to section b of known x-coordinate Columbian friction coefficient of the workpiece-die is μ, and the workpiece yield strength from uniaxial tension is Y (ignore elastic strain) A. Determine the extrusion force F if we...
3 ) Consider a small Ax by Ay material element in a thin plate. The state of stress in the plate is specified by four components ơxx, Ơyy and Ơxy-o,r, and the state of strain is specified by Exx. Eyy and Exy Eyx. The other components are zero. Let the x-component of the body force acting on the body be Fx, show that the equation of equilibrium for the element in the x-direction is (ii) Given the constitutive relation between...
The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: Question 2 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: o. O40000 L0 80 230 ay a. Calculate the strain tensor b. Calculate the characteristic equation for the three-dimensional state of strain. c. Calculate the principal strains at the point. d. Calculate the volumetric strain and the deviatoric strain invariants The material...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
need solution for milestones A Q1 Solid Mechanics 3 Assessment Task 1a - 2020 Milestone a Question 1. For each of the plane-stress conditions given below, construct a Mohr's circle of stress, find the principal stresses and the orientation of the principal axes relative to the xy axes and determine the stresses on an element, rotated in the x-y plane 60° counterclockwise from its original position: (a) dx = 200 MPa Oy - 300 MPa T .40 MPa (b) dx...