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Plate With a Hole Tutorial - Pre-Analysis and Start-Up

How to solve this Problem

Analytical vs. Numerical Approaches

We can either assume the geometry as an infinite plate and solve the problem analytically, or approximate the geometry as a collection of "finite elements", and solve the problem numerically. The following flow chart compares the two approaches. There are two main methods to solve this problem. Refer to the diagram below:

https://confluence.cornell.edu/download/attachments/127122289/FlowLarge.png?version=1&modificationDate=1320261775000

As seen in the flow chart, we can either assume the geometry as an infinite plate and solve the problem analytically, or we approximate the geometry as a collection of finite elements, and solve the problem numerically. First, we will assume the plate is infinite and will complete the analytical calculations.

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Let's first review the analytical results for the infinite plate. We'll then use these results to check the numerical solution from ANSYS.

Analytical Results

Displacement

First, let's estimate the total expected displacement of the bar. To this, we will estimate the plate with a hole as a tensile bar with a constant cross sectional arearight edge relative to the center of the hole. We can get a reasonable estimate by neglecting the hole and approximating the entire plate as being in uniaxial tension.

NowSubstituting values, subbing in values

sigma_xx

First, let's begin by finding the average stress, the nominal area stress, and the maximum stress with a concentration factor.

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