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Problem 1 (45 points) The state of stress in a thin sheet of an engineering polymer can be expressed by cartesian components bij relative to the basis vectors {e;} by [] S T 0 TS 0 0 0 0 for parametric values S and T of dimension stress.
(15 points) Isotropic elastic constants of the material are Young's modulus, E, and Poisson ratio, v. A strain gage is bonded on the surface of the plate, oriented in a direction parallel to the unit vector n= cos teu + sin 8e2. - (7 points) Obtain a symbolic expression for the value of the strain, Egage (), which will be recorded by the strain gage under the imposed state of stress. Express your answer in terms of 0, elastic constants, and the stress values S and T =rxS. - (8 points) Use this result to determine the gage orientation * = Ô* (r) which gives local maxima and minima for égage@). Do the resulting strain gage directions n* = cos(0*(r)e + sin(0*(r)e2, have any special relationship with any of the eigenvectors e of the stress tensor, as determined above? Discuss. =