The wedge shaped bar shown in Figure Q1 is to be analysed using a single one dimensional quadratic element as shown. The bar has a rectangular cross section with a constant width and a linearly varying depth. un 1 k= 10E-25 211 He 500 + 712' 2 100 a) Calculate the strain shape function matrix, [B], for the element. b) Using the strain shape function matrix derived in (a), show that the stiffness matrix for the element is given by the equation: I 1. Ֆ. Մ. 3 Figure Q1. 112 h -25 5+1 (3- d M 100- ALL DIMENSIONS IN mm with units of N/mm of the material 10 Where: E = Young's modulus c) Show how the strain shape function matrix may be used to determine the stress from the nodal displacement for this type of element. Do not attempt to calculate the stress.

The wedge shaped bar shown in Figure Q1 is to be analysed using a single one dimensional quadratic element as shown. The bar has a rectangular cross section with a constant width and a linearly varying depth. un 1 k= 10E-25 211 He 500 + 712' 2 100 a) Calculate the strain shape function matrix, [B], for the element. b) Using the strain shape function matrix derived in (a), show that the stiffness matrix for the element is given by the equation: I 1. Ֆ. Մ. 3 Figure Q1. 112 h -25 5+1 (3- d M 100- ALL DIMENSIONS IN mm with units of N/mm of the material 10 Where: E = Young's modulus c) Show how the strain shape function matrix may be used to determine the stress from the nodal displacement for this type of element. Do not attempt to calculate the stress.

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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