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In this study, we present a novel finite element approach to simulate crack propagation in shell structures. A local spider-web mesh is placed at the tip of a crack propagating through a global background mesh. Interface shell elements with assumed natural strains are used to connect a non-matching interface between the background mesh and the local spider-web mesh. Interface shell elements are also employed for trimmed shell elements created by cutting shell elements with the crack line. Numerical simulation of crack propagation in shell structures can be easily performed by moving the local spider-web mesh with an incremental crack growth. Numerical experiments show that the present method is very efficient and effective to accurately simulate crack propagation in shell structures without significantly increasing computational burden and implementation complexity of remeshing process.

In this study, a new polygonal shell element is developed to provide greater flexibility in mesh design of complex shell structures . Wachspress coordinates are used to construct shape functions for polygonal shell elements. An assumed covariant shear strain field with respect to the element natural coordinate system is defined by employing the mixed interpolation of tensorial components approach to avoid transverse shear locking in polygonal shell elements. Moreover, an assumed covariant membrane strain field is constructed by using characteristic geometry and displacement vectors defined on quadrilateral subdomains of polygonal shell elements to alleviate membrane locking due to the element curvature. Some benchmark shell problems are solved to evaluate the performance of the proposed polygonal shell elements. Numerical experiments show that they converge much better than triangular shell elements and comparable to quadrilateral shell elements.

In this paper, a novel level set-based topology optimization method for shell structures is presented to minimize both compliance and stress under a volume constraint. During the optimization process, trimmed quadrilateral shell meshes are generated by cutting a background quadrilateral shell mesh with the zero-isolines of a level set function. Polygonal shell elements with assumed strains are used for the trimmed quadrilateral shell elements created along the boundaries of shell structures. A new sensitivity field for the evolution of a level set function is proposed to minimize both compliance and stress of shell structures. A p -norm function is employed to aggregate local stresses into a single global stress measure in the sensitivity analysis. Several numerical examples are carried out to show the validity and effectiveness of the proposed method.

In this study, a novel interface shell element (ISE) is developed based on a variable-node element formulation to couple non-matching quadrilateral shell meshes. Shape functions for ISEs are explicitly presented in a polynomial form with the use of appropriate supports of weight functions in moving least square (MLS) approximation. Assumed natural strains in the form of the mixed interpolation of tensorial components (MITC) approach are employed to avoid the transverse shear locking when the thickness of shell tends to zero. Moreover, an assumed membrane strain field defined over quadrilateral subdomains subdividing an ISE is used to alleviate the membrane locking in curved ISEs. Numerical experiments show the effectiveness and efficiency of ISE for connecting dissimilar quadrilateral shell meshes at a common interface.

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 bou...

In this study, a novel scheme for modelling and analysis of spot-welded shell structures is presented by placing local spider-web shell meshes representing the weld nugget region in a global shell mesh. Interface shell elements are employed for trimmed shell elements with arbitrary number of nodes created by cutting a global shell mesh with the boundaries of local spider-web shell meshes. Transverse shear and membrane locking phenomena in interface shell elements are effectively alleviated by introducing assumed natural strain fields. Conventional elastic beam elements with six degrees of freedom are used to connect the center nodes of local spider-web shell meshes. The present method can construct high-quality shell meshes around spot welds without any global remeshing, which makes it very efficient and effective for the analysis of spot-welded shell structures.