The integrations needed to determine beam deflections require the enforcement of the appropriate displacement and rotation boundary conditions (BCs). It is important that we be able to recognize these ...

In civil engineering, flexural beams are used to control the effect of vibrations that can cause cracks to appear in surfaces (concrete slabs) and beams. This is particularly important in buildings ...

Thin films form the basis of many industries today, including semiconductors, electric vehicles, smart optical coatings, sophisticated medical equipment, and protective layers on high-temperature ...