Application of the Finite Element Method Using MARC and Mentat 3-1 Chapter 3: Tapered Bar Keywords: 1D elasticity, 2D elasticity, plane stress, model symmetry, convergence Modeling Procedures: ruled surface, convert 3.1 Problem Statement and Objectives A tapered bar subjected to an axial load will be analyzed in order to predict the distributions of stress and displacement in the bar. The geometrical, material, and loading specifications for the bar are given in Figure 3.1. The thickness of the bar is 2h inches, where h is described by the equation: h x x = - + 4 0 6 0 03 2 . . 3.2 Analysis Assumptions • Because the bar is thin in the width (out-of-plane) direction, a state of plane stress can be assumed. • Even though the load is exclusively axial, the taper in the bar may cause the state of stress to be two-dimensional in nature. The effect of taper on the stress state depends upon the degree of the taper, and is difficult to assess a-priori. Therefore, both a 2D plane stress elasticity analysis and a 1D elasticity analysis will be performed. Geometry: Material: Steel Length: L=10” Yield Strength: 36 ksi Width: b=1” (uniform) Modulus of Elasticity: 29 Msi Thickness: 2h (a function of x) Poisson’s Ratio: 0.3 Density = 0.0088 slugs/in 3 Loading: Axial Load: P=10,000 lbs Figure 3.1 Geometry, material, and loading specifications for a tapered bar. P 2h L x
Chapter 3: Tapered Bar
Jun 21, 2023
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