Aero 405 Test

Where do principal shear stresses occur?

On planes rotated 45 degrees away from the principal stress planes

How are principal stresses determined form the shear tensor?

Principal stresses are the eigenvalues of the stress tensor matrix.

What is Stress as a physical concept and a tensor.

It is a mathematical representation of every possible traction acting on every possible surface within a material.

Shear stress acts ___ to the surface

parallel

In finite element assembly, if an external distributed load $t$ is applied to an outer boundary surface, what does the term sigma dot n_hat evaluated on that surface represent?

The internal stress balancing the load.

What is the Penalty Method

An optimization technique designed to enforce a design to stay inside its required bounds by actively penalizing bad designs.

When is the penalty method used?

This method is applied when the original objective function does not intrinsically consider constraints on its own. Adding the penalty term mathematically forces the search to evaluate and respect the problem's boundaries.

Describe the plane stress assumption and name two types of structural components for which this assumption applies. (4 pts)

Plane stress assumes that all stresses acting on the element are in the xy plane. Valid for thin elements (membranes)

Refer to image.

A designer is considering two design variables x and y, and desires to perform six finite element analyses. Carefully and neatly show (as a 2-D plot in x − y space) an example LHS sampling that provides six possible {x, y} combinations that could be considered.

In the context of this course, design optimization describes the process of minimizing a ______ function ( ____ function), subject to the satisfaction of ___ functions, which represent design requirements. We do this by varying design ____, for which we assume meaningful maximums and minimums known as bounds.

objective, cost, , constraints