A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature

The point load static problem for structural components is a classic numerical test that can be found in several finite element benchmarks throughout the literature. In finite element analysis, since the solution is found in integral form within each element, concentrated forces can be applied at every mesh node. On the contrary, collocation methods do not admit to apply concentrated forces at their collocation points, since only smooth and continuous functions can be discretized. Exploiting a mixed approach of integral and differential quadrature it is possible to treat concentrated loads using Dirac-delta function. Thus, this paper shows convergence, stability and accuracy of the present approach when applied to beams, plates and doubly-curved thin and thick shells. The GDQ method is considered, in particular the best grid point collocation is found in order to achieve the best accuracy using Dirac-delta function. In addition, an alternative approach is presented for the first time, simulating a point load using a continuous and smooth normalized Gaussian distribution.