Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

A systematic development of 'solid-shell' element formulations for linear and non-linear analyses employing only displacement degrees of freedom

Abstract: In the present contribution we propose a so-called solid-shell concept which incorporates only displacement degrees of freedom. Thus, some major disadvantages of the usually used degenerated shell concept are overcome. These disadvantages are related to boundary conditions—the handling of soft and hard support, the need for special co-ordinate systems at boundaries, the connection with continuum elements—and, in geometrically non-linear analyses, to a complicated update of the rotation vector. First, the kinematics of the so-called solid-shell concept in analogy to the degenerated shell concept are introduced. Then several modifications of the solid-shell concept are proposed to obtain locking-free solid-shell elements, leading also to formulations which allow the use of general three-dimensional material laws and which are also able to represent the normal stresses and strains in thickness direction. Numerical analyses of geometrically linear and non-linear problems are finally performed using solely assumed natural shear strain elements with a linear approximation in in-plane direction. Although some considerations are needed to get comparable boundary conditions in the examples analysed, the solid-shell elements prove to work as good as the degenerated shell elements. The numerical examples show that neither thickness nor shear locking are present even for distorted element shapes. © 1998 John Wiley & Sons, Ltd.

Iterative methods for variational and complementarity problems

Abstract: In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

Optimum Uniform Piecewise Linear Approximation of Planar Curves

Abstract: Two-dimensional digital curves are often uniformly approximated by polygons or piecewise linear curves. Several algorithms have been proposed in the literature to find such curves. We present an algorithm that finds a piecewise linear curve with the minimal number of segments required to approximate a curve within a uniform error with fixed initial and final points. We compare our optimal algorithm to several suboptimal algorithms with respect to the number of linear segments required in the approximation and the execution time of the algorithm.

On the excitation of long nonlinear water waves by a moving pressure distribution

Abstract: A study is made of the wave disturbance generated by a localized steady pressure distribution travelling at a speed close to the long-water-wave phase speed on water of finite depth The linearized equations of motion are first used to obtain the large-time asymptotic behaviour of the disturbance in the far field; the linear response consists of long waves with temporally growing amplitude, so that the linear approximation eventually breaks down owing to finite-amplitude effects A nonlinear theory is developed which shows that the generated waves are actually of bounded amplitude, and are governed by a forced Korteweg-de Vries equation subject to appropriate asymptotic initial conditions A numerical study of the forced Korteweg-de Vries equation reveals that a series of solitons are generated in front of the pressure distribution