- CFD, Fluid Flow, FEA, Heat/Mass Transfer

Navier-Stokes Equation for Solid Deformation

Bending of a trapezoidal plate or tapered beam subject to uniform pressure 'p':

No analytical expression exists for these integrals. However, it can be integrated analytically if the tapered beam ends at zero widths (sharp edge) and is shifted to the tip instead of the base. In this case, B

For bending of circular disk supported at one of its diameter and under uniform pressure 'p', H = thickness of the plate and symmetric half is shown below:

The deflection at any location x is given by:

- Pre-load = tension in bolt (due to tightening) as net elongation of bolt which is difference of change in length of the bolt and compression of the clamped member.
- Service Load = external force acting on the clamped member.
- Bolted-joint Diagram: this is a "external force" vs. "bolt elongation" curve used to describe variation in clamping force with respect to applied force.

The for loop to implement the steps and index notation defined above is as follows.

The same operation using transpose of a matrix can be implemented in a bit different manner as shown below.

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