BE_110_HW_Excercise_ - ≤ x,y ≤ 1 for the following function Φ(x,y =(x 2 y x y 2 Plot the stress field in graphical format 4 Show that if the

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BE 110 An Introduction to Biomechanics Fall 2005 This homework set is for practice only. You do not need to turn it in for grading. 1. Let τ ij be the stress tensor. What is the physical interpretation of the following quantities: (a) τ 33 (b) τ 13 (c) -(1/3) τ ij δ ij (d) τ ij υ i where δ ij is the Kronecker symbol and υ i is a unit vector. 2. What is the physical interpretation of the expression β ik β jk = δ ij where β ij is an orthogonal transformation and δ ij the Kronecker symbol. 3. Consider a two-dimensional state of stress in a thin plate in which τ zz , τ zx , τ zy are zero. The plate is in equilibrium. Show that the stresses derived from a continuously differentiable Airy stress function Φ (x,y) such that τ x = 2 Φ y 2 y = 2 Φ x 2 xy =− 2 Φ x y also satisfies the equilibrium conditions in the absence of a body force. Note, this is an important result in solid mechanics from which many solutions have been derived for beams and plates. Find the stresses on a plate with coordinates -1
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Unformatted text preview: ≤ x,y ≤ 1 for the following function Φ (x,y) = (x 2 y + x y 2 ). Plot the stress field in graphical format. 4. Show that if the stress components τ ij in one coordinate system are equal to zero, they are equal to zero in all other coordinate systems. What are the values of the stress invariants, I 1 , I 2 , I 3 ? 5. Find the resultant moment distribution in the foot of a diving athlete with weight W standing upright on a platform just before the jump. The athlete is standing on the edge of the platform supported only by the toes without support on the heels. The length of the foot from the heel to the base of the toes is L. _____________________________________________________________________________ Please note the Midterm will be on November 3, 2005, from 8AM to 9:20AM (closed book and no electronic device)....
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This note was uploaded on 03/26/2010 for the course BENG 110 taught by Professor Schmid-schoenbein during the Spring '08 term at UCSD.

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