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being stretched it occupies the interval 0

being stretched it occupies the interval 0

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem # 1 A linearly elastic bar is made of two different materials, and before being stretched it occupies the interval 0 SASlo. Also, before being stretched, for OSA< A0, the modulus and density are E = E, and R = R1, while for A,< A < l, they are E = Egand R = Rg. Both R, and Rg are constants. (Hint: It is useful to define separate functions UL(A), UR(A), T¿(A), TR(A), etc. on the left and right parts of the domain.)e (a) The requirements at the interface, where A = A, are that the displacement and stress are continuous. Express these requirements mathematically, using one-sided limits. (b) Suppose the bar is stretched and the boundary conditions are U(0, t) = 0 and U(, t) =l – lo. Assume there are no body forces. Find the steady state solution for the density, displacement and stress. «
Transcribed Image Text:Problem # 1 A linearly elastic bar is made of two different materials, and before being stretched it occupies the interval 0 SASlo. Also, before being stretched, for OSA< A0, the modulus and density are E = E, and R = R1, while for A,< A < l, they are E = Egand R = Rg. Both R, and Rg are constants. (Hint: It is useful to define separate functions UL(A), UR(A), T¿(A), TR(A), etc. on the left and right parts of the domain.)e (a) The requirements at the interface, where A = A, are that the displacement and stress are continuous. Express these requirements mathematically, using one-sided limits. (b) Suppose the bar is stretched and the boundary conditions are U(0, t) = 0 and U(, t) =l – lo. Assume there are no body forces. Find the steady state solution for the density, displacement and stress. «
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