A new strategy for finite‐element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

Abstract

Summary In this paper, we present a novel scheme to generate trimmed quadrilateral shell meshes using a paving and cutting algorithm. Paving with well‐shaped quadrilateral shell elements is initiated from a seed element placed in the interior of a geometric surface and proceeds around the boundary of the paved mesh in all directions. The paved all‐quadrilateral mesh covering the entire domain is cut by the boundaries of a geometric surface. Pentagonal shell elements are created by cutting the corners of quadrilateral shell elements at the domain boundaries. Pentagonal shape functions are constructed using Wachspress coordinates, and assumed natural strains in the form of the mixed interpolation of tensorial components approach are employed to avoid the transverse shear locking of pentagonal shell elements. Several numerical examples are investigated to show the effectiveness of the present method.

Coupling design and fabrication of continuous carbon fiber-reinforced composite structures using two-material topology optimization and additive manufacturing

“…As described in section 2, in the two-material topology optimization process of CCF-reinforced composite structures, the structural boundaries of the resin material and fiber reinforcement are represented by the zero-contour of level set functions. To accurately represent the structural boundary of an optimal design, the cutting method, presented in two of the authors' works [42,[46][47][48][49][50], is used. In this method, the zero-contour of level set functions k,i .…”

Best theory diagrams for multilayered structures via shell finite elements

“…Over the last decades, the research activity has focused on the development of shell and plate models incorporating the effects mentioned above [9,10]. Most recent efforts describe well the open research topics and refinement techniques related to shells, such as, improvements of classical models [11] and higher-order models [12][13][14]; asymptotic approaches [15]; improvement of FE performances regarding membrane and shear locking [16][17][18][19][20][21], mesh accuracy [22], and distortion [23]; improved modeling of the interlaminar shear stresses [24]; Layer-Wise (LW) models [25,26]; Zig-Zag models [27,28]; mixed formulations [29][30][31]; variable kinematics finite elements with multifield effects [32]; extensions to non-linear problems [33,34] and peridynamics [35]; innovative solution schemes such as the numerical manifold method [36].…”