Incremental Finite Element Method Research Articles

On a numerical simulation for stable crack extension process and a nonlinear fracture criterion

In this note a numerical simulation for a stable crack extension process has been worked out by an incremental finite element method. Utlizing the critical opening angle at the crack tip and accounting for the effect of stress history, we have visualized the stable crack extension process from initiation to instability. Several field variables including J- integrals , stresses and strains, have been computed for every incremental load step. It appears that the critical opening angle at the crack tip may serve as an important parameter in these fracture phenomena including the stable crack extension process. Based on the numerical results an idea for a nonlinear fracture criterion is proposed.

ON CHARACTERISTICS OF THE SNAP-THROUGH ACTION OF COMPLEX ARCH SPRINGS : 3RD REP., THERMAL CHARACTERISTICS OF UNIT ARCH SPRINGS AND MOVABLE BIMETALLIC SPRINGS OF THERMOSWITCHES

By using the incremental finite element method with triangular plane elements, the snap-through action problems due to thermal expansion of the unit arch spring and the complex ones are analyzed. Then, for the purpose of analyzing the action of the bimetallic arch spring as a typical example of these springs, an effective method with beam-column elements is proposed. The latter method is applied in analyses of the thermal snap-through action of the U- and W-type bimetallic springs for thermoswitches. Then by examining several numerical results by the method of experimental designs, some design formulae for the U-type bimetallic spring are obtained.

ON CHARACTERISTICS OF SNAP-THROUGH ACTION OF COMPLEX ARCH SPRINGS : 1ST REP., STATICAL CHARACTERISTICS OF UNIT ARCH SPRING AND MOVABLE SPRING OF Z-TYPE MICROSWITCH

By using the incremental finite element method, the snap-through problem of the unit arch and that of the movable spring for the Z-type precision snap-acting switch (i.e. the microswitch) are analysis with sufficient accuracy in this report. The latter is treated as an example of the complex arch spring. Concerning the finite element formulation with beam-column elements, a new element model, the both ends of which are elastically supported on a fixed foundation, is proposed. By examining the numerical results by the method of experimental designs, some design formulae of the movable spring of the Z-type microswitch are obtained.

A Mixed Finite Element Method for Plasticity Problems with Hardening

We prove an error estimate for an incremental finite element method for plasticity with hardening. Stresses and displacements are approximated by piecewise constant and piecewise linear functions, respectively.

On finite element methods for plasticity problems

We prove an error estimate for an incremental finite element method for obtaining approximations to the stresses in an elastic-perfectly plastic body. We also comment on the limit load problem.

On the Strength of Structures with Imperfections (2nd Report)

The contents of this paper are summarized as follows.(1) The computer program based on incremental finite element method which had the layered triangular plate element and layered stiffener elemet as main elements was made to analyze nonlinear behaviours of plate structures including buckling collapse of plate structures with initial deflections.(2) The experiments of three girder models with initially deflected end corners were conducted to search buckling collapse loads and modes.(3) The comparison of the computed results with the experiments mensioned above showed good agreements on both collapse loads and modes. As the computing time required is not so long, the numerical analysis is considered to be applicable to obtain the tendency of the influences of initial deflections on the collapse.

Retaining Wall Under Action of Accreted Backfill

The purpose of this note is to demonstrate the dependence of the behavior of a rigid retaining wall on the construction sequence of the backfill. The accretion process was analyzed through an incremental finite element method with a nonlinear soil having the characteristics of Ottawa sand. Although a relatively simple analytical model was considered, other inclusions might have been: 1) the effects of flexibility of the wall; 2) more complicated interface conditions; 3) backfill compaction; and 4) various constitutive relationships for the soil, which may occur in future work.

Finite Element Method of Analysis of the Hydrostatic Bulging of a Sheet Metal (Part 1)

An incremental finite element method of the large elastic-plasic deformation of non-axisymmetric metal diaphragms which are edge-clamped and bulged by hydrostatic pressure has been formulated. The diaphragm is divided into a number of flat triangular elements and the behavior of a typical element is described in terms of the displacements of its nodes. The authors derive stiffness matrices, taking account of effects of shape change on the equilibrium equations, from a total differential of the equivalent nodal forces. In order to check the theory, numerical calculations were carried out for the bulging of a circular diaphragm under hydrostatic pressure. Theoretical results were in reasonable agreement with experiments for aluminium sheet and also with numerical solutions by means of a finite difference method.