A new variant of the fem for evaluation the strenght of structures of complex geometry with heterogeneous material structure

Structures are known to feature a complex geometry and a complex material structure which varies depending on their functional purpose, technological capabilities and design. The finite difference method, collocation method, variational method, theoretical and experimental method, finite element method, among other methods, are employed to calculate the stress-strain state (SST) of structures of complex geometry. The finite element method (FEM) has become the most common one of them all. The spline version of the finite element method (SV FEM) has proven to be an effective FEM method used to calculate the SST of structures of complex geometry. Unlike the conventional FEM method, a preliminary parametrization of the entire area of complex geometry using the parameters outlined by the canonical domain and a cubic approximation of the desired variables within each element yields consistent finite elements. The unbroken geometric continuity maintained between the elements along with the continuity of the desired quantities and their first derivatives along the line of contact of the elements makes it possible to obtain reliable results with just a small number of partitions into finite elements. One should note the application of the basics of the spline version of the finite element method in two-dimensional SV FEM-2 and three-dimensional SV FEM-3 arrangements. One should also make mention of the idea of producing a synthesized version of SV FEM. Two-dimensional and three-dimensional elements being synthesized into one element would usher in a new phase in the development of the SV FEM approach which would describe the complex structures of construction materials in addition to complex geometry. SV FEM has made it possible to evaluate the SST of structural elements of complex geometry along with the thin layers that penetrate it in all three directions. The versions of SV FEM that are available now serve to assess the SST of a broad range of various thin-walled and non-thin-walled structures of complex geometry, including multilayer structures with thin layers in all three directions, with hard and soft coatings along the edges and with local defects on the surfaces of structures. This paper presents a number of SST calculations of specific structures that have been carried out via the FEM versions described above.