homework 2D Elements

Engineering

IFS

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ME 474 / BME 488 Homework 8 Due: 04/13/2020 @ 6:00 PM When submitting this homework, include a pdf of your written work as well as any MATLAB (.m) or Excel (.xls, .xlsx) files used to solve the problems. Make sure your work is well documented and easy to follow. 1. We have used two-dimensional rectangular elements to model temperature distribution in a thin plate. The values of nodal temperatures for an element belonging to such a plate are given in the figure below. Using local shape functions, what is the temperature at the center of this element? 2. Two-dimensional triangular elements have been used to determine the stress distribution in a machine part. The nodal stresses and their corresponding positions for a triangular element are shown in the figure below. What is the value of stress at x = 2.15 cm and y = 1.1 cm? 3. Show that the area A of a triangular clement can be computed from the determinant of: 1 |1 1 𝑋𝑖 𝑋𝑗 π‘‹π‘˜ π‘Œπ‘– π‘Œπ‘— | = 2𝐴 π‘Œπ‘˜ ...
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