Navier-Stokes Equation for Solid Deformation
Differential equation of deflection curve:
Deflection by Area-Moment Method: distance of point B on a beam from tangent at point A on the beam is equal to the moment with respect to the vertical through B of the area of the bending moment diagram between A and B divided by flexural rigidity EIZ.
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, BZ(x) = BL × (x/L).
The deflection at any location x is given by:
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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