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assn10 - 1.050 Energy Bounds in Elasticity(HW#10 Due Friday...

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1.050: Energy Bounds in Elasticity (HW#10) Due: Friday, November 30, 2007 MIT – 1.050 (Engineering Mechanics I) Fall 2007 Instructor: Markus J. BUEHLER Team Building and Team Work: We strongly encourage you to form Homework teams of three students. Each team only submits one solution for correction. We expect true team work, i.e. one where everybody contributes equally to the result. This is testified by the team members signing at the end of the team copy a written declaration that "the undersigned have equally contributed to the homework". Ideally, each student will work first individually through the homework set. The team then meets and discusses questions, difficulties and solutions, and eventually, meets with the TA or the instructor. Important: Specify all resources you use for your solution. The following set of exercises is designed to familiarize you with the use of energy bounds in linear elasticity. This problem set is focused on 1D methods, and you will be able to apply the techniques you have learned in Lectures 27, 28 and 29. Please review the lecture notes and handouts carefully. For some of the solutions it is recommended to use Maple or Mathematica software to solve the resulting system of linear equations. 1. Truss structure : The sketch below shows a truss structure constructed with 6 vertical members and a horizontal rigid bar. The structure of subjected to two loads at points A and B (thus, this is a force-driven experiment). The top of the truss structure is connected to a fixed boundary. The goal of this problem is to solve for all displacements and axial forces using the structure’s energy content. L L L L L P Fixed boundary Rigid bar A B 2P
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Due: Friday – November 30, 2007 (in class) Page 2 of 7 r a. Proposed, approximate solution 1 : Use the displacement field ξ ' = ξ 0 ' e r z , which is displayed in the following sketch: P L L L L L z e r r ' ' 0 ξ
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