Computational methods for global/local analysis

Computational methods for global/local analysis of structures which include both uncoupled and coupled methods are described. In addition, global/local analysis methodology for automatic refinement of incompatible global and local finite element models is developed. Representative structural analysis problems are presented to demonstrate the global/local analysis methods

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement

Adaptive Element-Free Galerkin method applied to the limit analysis of plates

The implementation of an h-adaptive Element-Free Galerkin (EFG) method in the framework of limit analysis is described. The naturally conforming property of mesh- free approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. Nodes may be moved, discarded or introduced without the need for complex manipulation of the data structures involved. With the use of the Taylor expansion technique, the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy. A stabilized conforming nodal integration scheme is extended to error estimators and results in an efficient and truly meshfree adaptive method. To demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

A cell-based smoothed finite element method for kinematic limit analysis

This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged

3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks

A novel local mesh refinement approach for failure analysis of three-dimensional (3-D) linear elastic solids is developed, considering both 3-D straight and curved planar cracks. The present local mesh refinement formulation is in terms of the extended finite element methods and variable-node hexahedron elements, driven by a posteriori error indicator. Our 3-D formulation using hexahedron elements rigorously embraces a posteriori error estimation scheme, a structural coupling scale-meshes strategy and an enrichment technique. Remeshing is only performed where it is needed, e.g., a vicinity of crack, through an error estimator based on the recovery stress procedure. To treat the mismatching problem induced by different scale-meshes in the domain, a structural coupling scheme employing variable-node transition hexahedron elements based on the generic point interpolation with an arbitrary number of nodes on each of their faces is presented. The 3-D finite element approximations of field variables are enhanced by enrichments so that the mesh is fully independent of the crack geometry. The displacement extrapolation method is taken for the evaluation of linear elastic fracture parameters (e.g., stress intensity factors - SIFs). To show the accuracy and performance of our 3-D proposed formulation, six numerical examples of planar 3-D straight and curved shaped cracks with single and mixed-mode fractures and different configurations are considered and analyzed. The SIFs computed by the developed method are validated with respect to analytical solutions and the ones derived from the conventional XFEM. Associated with an adaptive process, the present 3-D formulation allows the analysts to gain a desirable accuracy with a few trials, which is suited for practices purpose

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes

Adaptive mesh refinements for thin shells whose middle surface is not exactly known

A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems