Parallel computing of high‐speed compressible flows using a node‐based finite‐element method

An efficient parallel computing method for high‐speed compressible flows is presented. The numerical analysis of flows with shocks requires very fine computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite‐element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of finite‐element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. The inter‐processor communication is minimized by renumbering the nodal identification number using ParMETIS. The numerical scheme for high‐speed compressible flows is based on the two‐step Taylor–Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic flows over a forward facing step. The numerical examples show that crisp shocks are effectively computed on multiprocessors at high efficiency. Copyright © 2003 John Wiley & Sons, Ltd.     

Generalized nodes and high‐performance elements

The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition‐of‐unity‐based finite‐element approximation. Construction of the partition‐of‐unity‐based approximation is accomplished by a physically defined local function of displacements. A 4‐node quadratic tetrahedral element and a 3‐node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition‐of‐unity‐based finite‐element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd.     

Finite element methodology for path integrals in fracture mechanics

Based on the energy foundation of the path-independent integral in non-linear fracture mechanics, I* integral as the dual form of Rice's J is presented, it is also path-independent and is equivalent to J in value but it relates to the complementary energy. It is proved that, in numerical implementation, the path independence of J and I* can be ensured by using the assumed displacement finite elements and the assumed stress finite elements, respectively. Regarding the bounds of crack parameters, it is demonstrated that the lower bound of J can be estimated by the displacement compatible elements, and the upper bound of I* can be estimated by the stress equilibrium elements. In view of the difficulties in formulating stress equilibrium model, instead of it, a quasi-equilibrium model is proposed, which makes hybrid stress elements be able to estimate the bound of I*, and do not lose the characteristics of stiffness formulation. Two four-node plane elements are suggested; of them, the incompatible one can be used in incompressible/fully plastic fracture analysis, and the penalty-equilibrium one can be implemented to estimate the bound of I*. Furthermore, an incremental formulation is developed for I*, and can be extended into the calculations of ductile fracture under monotonic loading. For attestation, quite a number of numerical experiments is carried out, and some significant results are offered. © 1998 John Wiley & Sons, Ltd.     

Stable and unstable crack growth in type 304 stainless steel plate

Experimental and theoretical results on stable as well as unstable fractures for Type 304 stainless steel plates with a central crack subjected to tension force are given.In the experiment using a testing machine with a special spring for high compliance, the transition points from the stable to the unstable crack growth are observed and comparisons are made between the test results and the finite element solutions.A round robin calculation for the elastic-plastic stable crack growth using one of the specimens mentioned above is also given.     

Allman's triangle,rotational DOF and partition of unity

A simplification of the 1984 Allman triangle (one of historically most important elements with rotational dofs) is presented. It is found that this old element takes a typical form of the partition of unity approximation. The Allman's rotation presented in the partition of unity form offers merits and convenience in formulation and practical applications. The stiffness matrix of the 1984 Allman triangle, which is originally computed from the linear strain triangular element (the 6 nodes quadratic triangle), can be obtained instead in a cheaper way from that of the constant strain triangular element. The constraint of the rotational terms during essential boundary treatment, which remains equivocal and ambiguous, is understood to be mandatory. The partition of unity notion enables a straightforward extension of the Allman's rotational dof to meshfree approximations. In numerical examples, we discuss suppression of spurious zero‐energy modes and patch tests. Standard benchmarks are carried out to assess performance of the newly formulated triangle and a meshfree approximation with the rotational dofs. Copyright © 2006 John Wiley & Sons, Ltd.     

Comments on “A conjugate-residual—FEM for incompressible viscous flow analysis”

Communicated by S. N. Atluri, April 1, 1989     

Risk–benefit analyses of SG tube maintenance based on probabilistic fracture mechanics

As an application of probabilistic fracture mechanics (PFM), a risk–benefit analysis was performed for the purpose of optimizing maintenance activities of steam generator (SG) tubes used in pressurized water reactors (PWRs). The probabilities of the SG tube leakage and rupture are defined as risks in this study. A model was made modifying pc-PRAISE (Piping Reliability Analysis Including Seismic Events) to evaluate the risks during 60 year operations due to stress corrosion cracking (SCC) of the tubes under various maintenance strategies for SG tubes.In the risk analysis, parameters such as inspection accuracy, inspection interval, sampling inspection and crack propagation law were selected for sensitivity analysis. Based on the risk analysis, a risk–benefit analysis was conducted when implementing two maintenance strategies taking both costs and revenues for 60 year operations into account. In the risk–benefit analysis, the expected cost of leakage or rupture was calculated by multiplying ‘probability of leakage or rupture’ by ‘expected loss of leakage or rupture accident’. To justify whether it is worthwhile implementing the maintenance strategies or not, the net present value (NPV) was calculated as an index, which is one of the most fundamental financial indices for decision-making based on the discounted cash flow (DCF) method.The results demonstrated that in the risk analysis, the risks are influenced significantly by the crack propagation law, accuracy of inspection and sampling inspection. In the risk–benefit analysis, it was suggested that investment to improve inspection accuracy would reduce the total costs of 60 year operations significantly and increase the NPV.Although the analysis was mainly conducted for SG tubes made of Inconel 600 mill anneal (MA) material, the analysis was also carried out for Inconel 690 thermal treatment (TT) material, making assumptions on its crack initiation and crack propagation law. In addition, the effect of introducing maintenance criteria, namely, operation with a crack justified by certain criteria, on NPV was evaluated.     

Performance study of the domain decomposition method with direct equation solver for parallel finite element analysis

A parallel performance of the domain decomposition method with directLDU algorithm of condensation and solution is studied. Typical subdomains arising after division of a square domain are considered, and operation count equations for all steps of the numerical procedure are derived. The parallel efficiency model is developed using operation count equations and message passing estimates. It is shown how to achieve interprocessor load balancing by partitioning a domain into unequal subdomains. The evaluation of the parallel efficiency model and performance studies for a square finite element domain are performed on the IBM SP2 computer with 4, 6 and 8 processor nodes. It is found that proper load balancing of the domain decomposition algorithm with direct solution of equation systems provides acceptable parallel efficiency for multiprocessor computers: 95% for the 6-processor configuration and 85% for the 8-processor configuration.