Método dos elementos finitos e design construtal aplicados à flambagem biaxial elasto-plástica de placas retangulares com furo oblongo

Abstract

Plate elements are commonly used in engineering structures in their most diverse aspects, especially in aeronautical and naval engineering, with emphasis on the construction of ship hulls and offshore structures. As they are slender structural structures with compression in the plane, they are related to elastic buckling, an unwanted phenomenon of structural instability. It is known that an elastic buckling does not cause a failure of the plates, as they have atypical behavior. Therefore, with the increase in external loading, the ultimate tension of the elastoplastic buckling is obtained. In addition, these structures often feature perforations, either to enable assembly, to mitigate structural weight or for aesthetic purposes. In this scenario, it is necessary to study the impact of these perforations on the plate elements. Therefore, in this work, the influence of longitudinal and centralized oblong perforations on the behavior of simply supported plates subjected to elasto-plastic buckling by biaxial compression will be analyzed. For the geometry of the plate, a ratio 𝑏/𝑎 = 0.5 was adopted, where b corresponds to width and length. The proposed oblong perforations were varied based on the following trends in volumetric fractions: ϕ = 0.10; 0.15; 0.20; where ϕ is the ratio of the volume of the plate and the volume of the perforation. In determining and analyzing the ultimate load of elasto-plastic buckling, the Finite Element Method (FEM) was adopted, designed to the shell element SHELL281 by the commercial software ANSYS® in association with the Design Construtal (DC) and Exhaustive Search methods, thus obtaining optimum geometries with better mechanical behavior. The plate of ϕ = 0.10 with aspect ratio 𝑏0/𝑎0= 0.2300 obtained the best Normalized Ultimate Stress (NUS) among all volumetric fractions. There was a greater possibility of improvement, of 29.21%, due to the variation of 𝑏0/𝑎0for the plates of ϕ = 0.20. In addition, it was observed that there is a trend between the geometries that lead to better performance to be stretched in the X direction. It was found a reduction in the mechanical resistance of the plates due to the presence of perforations. Keywords: Thin plates, biaxial elastoplastic buckling, Finite Element Method, Constructal Design.