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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. 500 2 211 100 k = 10E-25 -1 112 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: 3 Figure Q1. Lun X h = 100- - 10 ALL DIMENSIONS IN mm -12-25 5+21 (3-5)05 with units of N/mm Where: E = Young's modulus of the material 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. 500 2 211 100 k = 10E-25 -1 112 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: 3 Figure Q1. Lun X h = 100- - 10 ALL DIMENSIONS IN mm -12-25 5+21 (3-5)05 with units of N/mm Where: E = Young's modulus of the material 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
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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Question 1 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. 500 2 -12 100 k = 10E-25 -1 112 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: un 3 Figure Q1. 112 h = 100-X 10 ALL DIMENSIONS IN mm -25 ६+ +¹(3- (3-5) d with units of N/mm Where: E = Young's modulus of the material 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.
Transcribed Image Text:Question 1 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. 500 2 -12 100 k = 10E-25 -1 112 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: un 3 Figure Q1. 112 h = 100-X 10 ALL DIMENSIONS IN mm -25 ६+ +¹(3- (3-5) d with units of N/mm Where: E = Young's modulus of the material 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.
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