Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

A 17-node quadrilateral spline finite element using the triangular area coordinates

Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.

Data Mining and Machine Learning Methods Applied to A Numerical Clinching Model

Numerical mechanical models used for design of structures and processes are very complex and high-dimensionally parametrised.The understanding of the model characteristics is of interest for engineering tasks and subsequently for an efficient design.Multiple analysis methods are known and available to gain insight into existing models.In this contribution,selected methods from various fields are applied to a real world mechanical engineering example of a currently developed clinching process.The selection of introduced methods comprises techniques of machine learning and data mining,in which the utilization is aiming at a decreased numerical effort.The methods of choice are basically discussed and references are given as well as challenges in the context of meta-modelling and sensitivities are shown.An incremental knowledge gain is provided by a step-bystep application of the numerical methods,whereas resulting consequences for further applications are highlighted.Furthermore,a visualisation method aiming at an easy design guideline is proposed.These visual decision maps incorporate the uncertainty coming from the reduction of dimensionality and can be applied in early stage of design.

Patch test function for axisymmetric element of conventional and couple stress theory

The enhanced patch test proposed by Chen W J(2006) can be used to assess the convergence of the problem with non-homogeneous differential equations.Based on this theory,we establish the patch test function for axisymmetric elements of conventional and couple stress theories,and reach an important conclusion that the patch test function for axisymmetric elements cannot contain non-zero constant shear.