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# HW3 - EN222 Mechanics of Solids Homework 3 Dislocations Due...

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EN222: Mechanics of Solids Homework 3: Dislocations Due Thursday February 23, 2006 Division of Engineering Brown University 1. Set up a symbolic manipulation program to calculate the stresses induced by an edge dislocation at a depth h below the surface of a half-space, using the method outlined in class. Note that the program will need help to evaluate quantities like 0 '( ) z . In Maple, the way to do this is to calculate the derivative first, and then take the complex conjugates, etc afterwards, as follows > Omega0 := C*log(z): > dOmega0 := diff(Omega0,z): > dOmega0bar := conjugate(subs(z=conjugate(z),dOmega0)): It is simplest to derive expressions for ' , ' ω and '' in terms of 0 0 , ω and their derivatives by hand, and then use this procedure to evaluate the formulas for the stress. To check your solution, check that the boundary conditions are satisfied on the surface of the half- space. Then plot the variation of strain energy density and stress along the surface of the half-space as a function of 1 / x h . Show results for both 1 0

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HW3 - EN222 Mechanics of Solids Homework 3 Dislocations Due...

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