Mechanics Problems in Mathcad

As an example let’s consider the structural mechanics problem in Mathcad. You are to estimate the deflection of the single fixed at its ends beam with length L after application of concentrated force F, with distance a between the point of application and the left end of the beam . The following example illustrates the possibility of the practical application of some previously discussed functions and methods of Mathcad. Let’s consider the method of character integration. The method is based on the differential equation, that looks like y''=M(x)/(E*I). For the section to the left of the point of application of force F, M(x) is calculated in compliance with formula M(x)=F*(L-a)*x/L. For the section to the right of the application of force F, M(x) is calculated in compliance with formula M(x)=F*((L-a)*x/L-(x-a)). The solution is based on double integration and is shown in programme listing. In addition, calculation results comparative verification was carried out, comparison done in compliance with the results, gained after solving the analytical equation of the beam deflection.

Let’s consider the application of the method of finite differences for the given problem. Algorithm of calculation using the method of finite differences is analogous to the algorithm, previously discussed, and the calculation results are shown in the programme listing.

Mechanics Problems

Mechanics Problems

Mechanics Problems

Mechanics Problems

Mechanics Problems

Mechanics Problems

Mechanics Problems