An efficient Galerkin meshfree flat shell formulation is presented for the analysis of buckling behaviors of stiffened plate structures. Both plate bending and membrane deformations are approximated by the reproducing kernel particle method (RKPM). The governing equation is transformed into a weak form, and it is discretized by the scattered nodes. The stiffness matrix is numerically integrated with the nodal integration technique, i.e., the stabilized conforming nodal integration (SCNI). The RKPM and SCNI based flat shell modeling approach can address the shear locking problem. Additionally, the present discretization is further improved by involving a drilling rotation component, which is to effectively model the stiffeners. There are six degrees of freedom per node. A singular kernel is also introduced into a set of the interpolants to model the web/flange connection, as well as the imposition of the essential boundary conditions. A generalized eigenvalue problem is analyzed for evaluating buckling loads/modes of the stiffened plate structures. The accuracy of the numerical results and the effectiveness of the proposed method are examined through several numerical examples.

Buckling analysis of stiffened plate structures by an improved meshfree flat shell formulation

Investigation of transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of isotropic solids and orthotropic composites by an extended meshfree method is described. We adopt the recently developed extended meshfree radial point interpolation method (X-RPIM), which combines either the standard branch functions or the new linear ramp function associated with Heaviside functions to capture crack-tip behaviors. It is the first time the linear ramp function integrating into meshfree X-RPIM has been presented in a dynamical fracture context. We are particularly interested in exploring insight into the behaviors of DSIFs under dynamic impact loadings (e.g., step, blast and sine loading types) using our meshfree method. For some of these problems numerical examples have been performed using the new ramp functions, and the obtained results of DSIFs have also been compared with those using the standard enrichment functions under which the two schemes have the same setting. In each case it is found that the numerical solutions delivered using the X-RPIM associated with the ramp enrichments are in good agreement with those with the standard functions. The paper first describes formulations and then provides verification of our developed approach through a series of numerical examples in transient dynamic fracture for both solids and orthotropic composites. Illustration of scattered elastic stress waves propagating in the cracked body is depicted to take an insight look at the behavior of dynamic response.

Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments

Analysis of cracked plate using higher-order shear deformation theory: Asymptotic crack-tip fields and XIGA implementation

A buckling analysis of stiffened plates including curvilinear surfaces is carried out by an effective meshfree model. The buckling loads and modes computed by the present method are analyzed. Six degrees of freedom (6-DOFs) curved shell meshfree formulation in a convected coordinate system including a drilling rotation component is employed, which enables the assembly of curved shells for the modeling of more complex structures. By this formulation, the assembly of any arbitrary shape of geometry can be modeled in convected coordinates, while the 5-DOFs shell formulation suffers from the modeling of shell assemblies. Particularly, curved shells with straight stiffeners and plates with curvilinear stiffeners are considered. Furthermore, a twisted T-shaped structure where both web and flange have curvilinear geometry is analyzed. A meshfree discretization is employed, with which the reproducing kernel particle method is used as the meshfree interpolant. A boundary singular kernel method is adopted to precisely impose an essential boundary condition and to model folded shell geometries. The accuracy and effectiveness of the proposed method are demonstrated by several shell buckling problems for stiffened plate structures with curvilinear surfaces. The obtained meshfree results are compared with the linear and quadratic shell element results of finite element method ANSYS and discussed.

Application of 6-DOFs meshfree modeling to linear buckling analysis of stiffened plates with curvilinear surfaces

An element-free Galerkin meshless method for simulating the behavior of cancer cell invasion of surrounding tissue

A novel meshfree discretization technique in terms of the reproducing kernel particle method is presented for accurately evaluating mixed-mode intensity factors of cracked shear-deformable plates. Mindlin–Reissner plate theory is adopted to solve the cracked plates problem in the Galerkin formulation, considering transverse shear deformation. The diffraction method, visibility criterion and enriched basis are included in the generation of meshfree interpolants for the modeling of fracture. In this work, numerical integration is treated using the stabilized conforming nodal integration (SCNI) and subdomain stabilized conforming integration (SSCI). The J-integral (contour integral) is employed to analyze the fracture mechanics parameters. SCNI/SSCI is thus adopted to evaluate the contour integral and to split the original J-integral into symmetric and asymmetric J-integral values. They are calculated by decomposing the smoothed displacement, moment and shear force quantities into symmetric/asymmetric parts. In addition, a displacement ratio method is introduced to divide the asymmetric J-integral value into corresponding moment and shear force intensity factors. The accuracy of the intensity factors and the path-independent properties in mixed-mode fracture problems are critically examined through several numerical examples.

Accurate evaluation of mixed-mode intensity factors of cracked shear-deformable plates by an enriched meshfree Galerkin formulation

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Accurate evaluation of mixed-mode intensity factors of cracked shear-deformable plates by an enriched meshfree Galerkin formulation