International Journal for Numerical Methods in Engineering

Zhao, Chongbin; Hobbs, B. E.; Ord, A.; Peng, Shenglin; Mühlhaus, H. B.; Liu, Liangming

doi: 10.1002/nme.1372pmid: N/A

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time‐step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright © 2005 John Wiley & Sons, Ltd.

Reaz Ahmed, S.; Deb Nath, S. K.; Wahhaj Uddin, M.

doi: 10.1002/nme.1374pmid: N/A

Optimum design of tire‐tread sections is an important practical issue. However, useful study of the problem that can suggest a reliable guideline for determining the optimum tread sections had hardly been made in the past. The present paper describes a new analysis of the state of stresses in tire‐tread sections in contact with the road surface, taking special care of the boundary conditions. Based on the analysis, a method is proposed to determine the optimum tread shapes for avoiding lateral slippage between tires and roads. The displacement potential function formulation, an ideal mathematical model for the practical stress problems, has been used in conjunction with finite‐difference method of solution. For the present analysis, lateral slipping in absence of frictional resistance as well as the no‐slip conditions of the tire‐tread contact surface have been considered along with a large number of tread aspect ratios. The present computational approach proves to be a powerful tool for determining the optimum tread shapes for avoiding the lateral slippage of tire‐treads. Copyright © 2005 John Wiley & Sons, Ltd.

Kwon, Kie‐Chan; Park, Sang‐Hoon; Youn, Sung‐Kie

doi: 10.1002/nme.1384pmid: N/A

A new meshfree method for the analysis of elasto‐plastic deformation is presented. The method is based on the proposed first‐order least‐squares formulation for elasto‐plasticity and the moving least‐squares approximation. The least‐squares formulation for classical elasto‐plasticity and its extension to an incrementally objective formulation for finite deformation are proposed. In the formulation, equilibrium equation and flow rule are enforced in least‐squares sense, i.e. their squared residuals are minimized, and hardening law and loading/unloading condition are enforced pointwise at each integration point. The closest point projection method for the integration of rate‐form constitutive equation is inherently involved in the formulation, and thus the radial‐return mapping algorithm is not performed explicitly. The proposed formulation is a mixed‐type method since the residuals are represented in a form of first‐order differential system using displacement and stress components as nodal unknowns. Also the penalty schemes for the enforcement of boundary and frictional contact conditions are devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near contact interface. The proposed method does not employ structure of extrinsic cells for any purpose. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Bindel, David S.; Govindjee, Sanjay

doi: 10.1002/nme.1394pmid: N/A

Electromechanical resonators and filters, such as quartz, ceramic, and surface‐acoustic wave devices, are important signal‐processing elements in communication systems. Over the past decade, there has been substantial progress in developing new types of miniaturized electromechanical resonators using microfabrication processes. For these micro‐resonators to be viable they must have high and predictable quality factors (Q). Depending on scale and geometry, the energy losses that lower Q may come from material damping, thermoelastic damping, air damping, or radiation of elastic waves from an anchor. Of these factors, anchor losses are the least understood because such losses are due to a complex radiation phenomena in a semi‐infinite elastic half‐space. Here, we describe how anchor losses can be accurately computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any non‐zero angle of incidence. We exploit the interpretation of the PML as a complex‐valued change of co‐ordinates to illustrate how one can come to a simpler finite element implementation than was given in its original presentations. We also examine the convergence and accuracy of the method, and give guidelines for how to choose the parameters effectively. As an example application, we compute the anchor loss in a micro disk resonator and compare it to experimental data. Our analysis illustrates a surprising mode‐mixing phenomenon which can substantially affect the quality of resonance. Copyright © 2005 John Wiley & Sons, Ltd.

Vijalapura, Prashanth K.; Govindjee, Sanjay

doi: 10.1002/nme.1399pmid: N/A

This paper deals with the design and implementation of an adaptive hybrid scheme for the solution of highly non‐linear, strongly coupled problems. The term ‘hybrid’ refers to a composite time stepping scheme where a controller decides whether a monolithic scheme or a fractional step (splitting) scheme is appropriate for a given time step. The criteria are based on accuracy and efficiency. The key contribution of this paper is the development of a framework for incorporating error criteria for stepsize selection and a mechanism for choosing from splitting or monolithic possibilities. The resulting framework is applied to silylation, a highly non‐linear, strongly coupled problem of solvent diffusion and reaction in deforming polymers. Numerical examples show the efficacy of our new hybrid scheme on both two‐ and three‐dimensional silylation simulations in the context of microlithography. Copyright © 2005 John Wiley & Sons, Ltd.