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(Solved): Problem 1. Consider the problem of finding the axial displacement of a truncated solid cone of len ...



Problem 1. Consider the problem of finding the axial displacement of a truncated solid cone of length \( L \) hanging under iFigure 1: Tapered hanging bar

Problem 1. Consider the problem of finding the axial displacement of a truncated solid cone of length hanging under its own weight and subjected to a downward load at the tip as show in Fig. 1. The diameter at the top is and changes linearly to at the bottom. The BVP of this problem is as follows: (a) Derive a suitable weak form for use with the Galerkin method. Clearly indi cate how the boundary conditions will be handled. (b) Starting with a quadratic solution, obtain an approximate solution of the problem using MATLAB ( 5 extra points to develop the code) or Mathematica (similar codes are shared in Canvas). Submit the code and results. Consider , and . Figure 1: Tapered hanging bar


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(a) The weak form for this problem can be derived by multiplying the differential equation by a test function, v(x), and integrating over the domain:?
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