Q. 2 Consider the beam shown below F = Q(x) L The differential equation for...
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Q. 2 Consider the beam shown below ΕΙ F = Q(x) L The differential equation for transverse deflection w of the beam is valid for the given problem. d² d²w ΕΙ (₁ dx² dx²-9(x) = 0 a) Write the required nodal variables of element (uº). b) Assume the interpolation function such that w = C₁ + ₂x + C3x² + C₁x³ Find the nodal variable by using the above interpolation function. c) Write the equations obtained in part (b) in matrix form such that {U} = [A] {C} d) Calculate [A]-¹ using Matlab symbolic programming. (1 mark) (2 marks) (2 marks) (2 marks) e) Calculate the shape functions by {N} = {X} × [A]-¹ f) Plot the value of shape functions for 0 ≤ x ≤ 1. Take L = 1 for plotting g) Calculate the local stiffness matrix [K]e -Le [K]e = √ [²] dx² h) Calculate the local force vector {F}e ΕΙ Le = ["" N₁ Ső 0 {F}e = [²]dx N₁ F dx Q. 2 Consider the beam shown below ΕΙ F = Q(x) L The differential equation for transverse deflection w of the beam is valid for the given problem. d² d²w ΕΙ (₁ dx² dx²-9(x) = 0 a) Write the required nodal variables of element (uº). b) Assume the interpolation function such that w = C₁ + ₂x + C3x² + C₁x³ Find the nodal variable by using the above interpolation function. c) Write the equations obtained in part (b) in matrix form such that {U} = [A] {C} d) Calculate [A]-¹ using Matlab symbolic programming. (1 mark) (2 marks) (2 marks) (2 marks) e) Calculate the shape functions by {N} = {X} × [A]-¹ f) Plot the value of shape functions for 0 ≤ x ≤ 1. Take L = 1 for plotting g) Calculate the local stiffness matrix [K]e -Le [K]e = √ [²] dx² h) Calculate the local force vector {F}e ΕΙ Le = ["" N₁ Ső 0 {F}e = [²]dx N₁ F dx
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a The required nodal variables of element u are displacement u at the start point and displacement u at the end point b The interpolation function for ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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