NURBS based least‐squares finite element methods for fluid and solid mechanics

This contribution investigates the performance of a least‐squares finite element method based on non‐uniform rational B‐splines (NURBS) basis functions. The least‐squares functional is formulated directly in terms of the strong form of the governing equations and boundary conditions. Thus, the introduction of auxiliary variables is avoided, but the order of the basis functions must be higher or equal to the order of the highest spatial derivatives. The methodology is applied to the incompressible Navier–Stokes equations and to linear as well as nonlinear elastic solid mechanics. The numerical examples presented feature convective effects and incompressible or nearly incompressible material. The numerical results, which are obtained with equal‐order interpolation and without any stabilisation techniques, are smooth and accurate. It is shown that for p and h refinement, the theoretical rates of convergence are achieved. Copyright © 2014 John Wiley & Sons, Ltd.     

不可压缩橡胶圆柱的空穴和分叉

利用Y.C.Gao给出的一类应变能函数,分析了不可压缩橡胶圆柱受静载荷作用时在等温条件下及有温度场分布时空穴产生的问题,给出了存在分叉解的条件,确定了外载荷与空穴半径的函数关系,研究了空穴形成时应力的分布,讨论了本构参数和温度对极限载荷和应力分布的影响.结果表明:当本构参数满足O＜n＜1时,橡胶圆柱体存在分叉解;由Neo-Hooken材料构成的圆柱体将会很稳定而不存在分叉解;本构参数n越大,材料越不容易发生孔洞化不稳定现象;温度越高,材料越不稳定.     

三元不可压粘性流数值计算的尝试

为了能在中型机上进行三元粘性流数值计算,本文用省内存,计算速度快的跳点法进行了三元粘性流的数值计算试验。计算表明这种差分格式用在三元粘性流计算上是可行的。     

Dynamical problem for an incompressible laminated cylinder with helical anisotropy. Part 1. Theory

Exact analytical solutions have been obtained of a one-dimensional dynamical problem for an incompressible elastic radially inhomogeneous helically orthotropic thick-walled cylinder under plane strain conditions, loaded with nonsteady internal or external pressure. Necessary and sufficient conditions for the existence, uniqueness and physical adequacy of the solutions have been established. Convergence of wave solutions for slightly compressible cylinders to the analytical dependences obtained for incompressible cylinders has been analytically proved. __________ Translated from Problemy Prochnosti, No. 2, pp. 114–123, March–April, 2006.     

Recovering local equilibrium from three-dimensional compatible finite element solutions

We study the application to compressible and incompressible three-dimensional elasticity problems of the technique that we proposed in 2009 for the recovery of equilibrated stresses from compatible finite element solutions. The case of finite elements with linear displacement approximations, for which the partitioned systems of loads are not initially balanced in terms of rotational equilibrium, addressed in 2012, is also considered. The article includes a presentation of the implementation details, a study of the convergence in terms of the energy of the error, and a characterization of the solutions obtained.     

Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations

In the present contribution we extend a previously proposed so‐called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modifications necessary for hyper‐elastic or elastoplastic material laws are discussed. These modifications concern the right Cauchy–Green tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modified Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright © 2000 John Wiley & Sons, Ltd.     

New enhanced strain elements for incompressible problems

A new enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four‐node finite element, is initially presented. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analysing at the element level the deformation modes which form a basis for the incompressible subspace the extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently another new element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and non‐linear situations. Copyright © 1999 John Wiley & Sons, Ltd.