Crack identification of beam structures using homotopy continuation algorithm

An approach based on homotopy continuation algorithm is presented to identify the parameters of a cracked beam. Euler–Bernoulli finite beam element with a fully opened crack model is adopted to establish the dynamic equation of the structural system. In the inverse problem, the homotopy equation is derived from minimizing the error between the calculated and the simulated measured acceleration responses. The range of homotopy parameter is divided into a number of divisions. Newton iterative method is employed to estimate the solution at each of these division points. The solution at the last division point corresponds to the homotopy equation matching the objective function. Numerical simulations with a simply supported beam and two-span beam show that the proposed method is very accurate compared to an existing method for both single and multiple cracks identification. The effects of type of excitation, division of the homotopy parameter and measurement noise on the identified results are discussed. It is noted that there is no need for an accurate set of initial values with the proposed approach.     

Optimized partitioning of unstructured finite element meshes

We address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two-step approach is proposed, which combines a direct partitioning scheme with a non-deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non-deterministic heuristics, the optimization step is shown to produce high-quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one-dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.     

A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures

This paper presents the development of a highly efficient user-defined finite element for modelling the bolt-load distribution in large-scale composite structures. The method is a combined analytical/numerical approach and is capable of representing the full non-linear load-displacement behaviour of bolted composite joints both up to, and including, joint failure. In the elastic range, the method is generic and is a numerical extension of a closed-form method capable of modelling the load distribution in single-column joints. A semi-empirical approach is used to model failure initiation and energy absorption in the joint and this has been successfully applied in models of single-bolt, single-lap joints. In terms of large-scale applications, the method is validated against an experimental study of complex load distributions in multi-row, multi-column joints. The method is robust, accurate and highly efficient, thus demonstrating its potential as a time/cost saving design tool for the aerospace industry and indeed other industries utilising bolted composite structures.     

Application of the finite element technique to continuation problems of stationary fields

The paper deals with the application of the finite element technique to the extrapolation of stationary fields. The problem of continuation of the field potentials derived from the experimental data has been solved. The main idea is based on the application of one of the regularisation methods for solving an ill-conditioned, under- or overdetermined algebraic system of equations. Numerical calculations performed in the paper show the possible applications of the proposed method.     

Limit analysis of cracked structures by mathematical programming and finite element technique

Limit analysis of cracked structures using mathematical programming and finite element method is presented. This direct algorithm is based on a proposition of the modified Markov variational principle. The obtained upper bound formula is applicable with any kinematic admissible finite elements. The regularization of plastic dissipation function is performed to overcome the indetermination of the objective gradient in the rigid region and to realize a smooth transition of the objective function between the plastified and non-plastified regions. In order to simulate the singularity of crack-tip strain field for an ideal plastic model, the separate-point degenerated finite elements are used around the crack tips. This improves the precision of limit solutions. Numerical results of plane and axisymmetric cracked structures are extensively compared with analytic ones. The application of limit analysis in fracture mechanics is illustrated by an example. Received 25 November 1998     

Incremental finite element analysis of geometrically altered structures

A conceptually simple, general method is described for the finite element simulation of multi-stage construction and excavation processes, including recognition of nonlinear material behaviour. Anomalous results reported in the literature for simulation of excavation of elastic media are examined, and shown to result from the inconsistent determination of nodal excavation forces from element boundary stresses.     

A bubble‐inspired algorithm for finite element mesh partitioning

This paper presents a bubble‐inspired algorithm for partitioning finite element mesh into subdomains. Differing from previous diffusion BUBBLE and Center‐oriented Bubble methods, the newly proposed algorithm employs the physics of real bubbles, including nucleation, spherical growth, bubble–bubble collision, reaching critical state, and the final competing growth. The realization of foaming process of real bubbles in the algorithm enables us to create partitions with good shape without having to specify large number of artificial controls. The minimum edge cut is simply achieved by increasing the volume of each bubble in the most energy efficient way. Moreover, the order, in which an element is gathered into a bubble, delivers the minimum number of surface cells at every gathering step; thus, the optimal numbering of elements in each subdomain has naturally achieved. Because finite element solvers, such as multifrontal method, must loop over all elements in the local subdomain condensation phase and the global interface solution phase, these two features have a huge payback in terms of solver efficiency. Experiments have been conducted on various structured and unstructured meshes. The obtained results are consistently better than the classical kMetis library in terms of the edge cut, partition shape, and partition connectivity. Copyright © 2012 John Wiley & Sons, Ltd.     

A finite element solution program for large structures

A straightforward and general computer program for assembling and solving (using Gauss elimination technique) widely sparsed finite element matrix equations with very large bandwidth and capable of handling different degrees-of-freedom and variable bandwidth at different nodes, is described herein. The program assembles any type of finite elements having arbitrary number of nodes and each node may have differnt degrees-of-freedom. It requires only a small core memory in the computer, although a fast random access device is also needed. The two very important features of this program are (i) it does not store any zero submatrices within the band and (ii) during the solution of equations all operations dealing with zero submatrices within the band are automatically skipped and thus the savings of a considerable amount of disc storage space and computer time can be effected in many cases. Another feature is that many right hand sides can be handled simultaneously. Hence the program is very economical for structures having widely sparsed matrix equations. A listing of the computer program written in FORTRAN IV for CDC 6400 computer is readily available from the authors, but unfortunately could not be given here because of lack of space. The program is so general that it can be used to solve a wide class of finite element problems without actually having to understand fully the techniques behind it.     

A large-scale three-dimensional finite element analysis of incompressible viscous fluid flow

An efficient finite element scheme for large-scale three-dimensional flow analysis is proposed. Focus of attention is placed on the time integration algorithm and some techniques for the reduction of the storage requirement, including the one-point quadrature technique and an iterative matrix solver. Application to large-scale three-dimensional problems is given to demonstrate the feasibility of the proposed scheme.     

耦合板结构随机能量有限元分析

基于单频激励下导出的板的能量流分析方程,将其应用推广到板受随机激励的情形,提出了宽带随机激励下板的响应能量及功率流的计算公式。对考虑弯曲和纵波场耦合的板结构给出了计算能量有限元耦合矩阵的一般方法。用能量有限元法对受到两个不相关宽带白噪声激励力作用的L型板的能量响应和功率流进行了计算,结果反映了各波场的能量在空间上的分布和它们在各波场内的流动特性,其中弯曲波场的功率流显示出相向功率流发生汇集和改变流向的特点。对该耦合结构的响应用统计能量分析法进行了求解,其结果与能量有限元法计算结果间较好的一致性验证了随机激励下板的能量有限元分析应用的正确性。     

Frequency domain damage detection of plate and shell structures by finite element model updating

Plate- and shell-like elements are the main constituent of many engineering structures such as ships and airplanes. This paper develops a frequency domain model updating method using power spectral density function and seeks its viability in damage identification of plates and shells. The derivation of the sensitivity equation is exact and measured natural frequencies of few lower modes are used to overcome the drawbacks of incomplete measurement. The method is numerically examined in several damage cases. The robustness of method against measurement and mass modelling error is numerically assessed using Monte-Carlo analysis and numerically simulated error contaminated data. The method proves to be robust against both kind of errors and performs well, both in cases of plate and shell elements.     

Elastic-plastic finite element analysis of thermally loaded cracked structures

Two elastic-plastic fracture parameters are considered here,J* and a direct evaluation of the potential energy release rate,G. Both parameters are evaluated from elastic-plastic finite element solutions of thermally loaded structures. The results show a reasonable agreement between the two parameters withG being numerically more stable.J* can be sensitive to mesh details and loading.

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Résumé On considère dans ce mémoire deux paramètres gouvernant une rupture élastoplastique, l'intégraleJ* et une évaluation directeG de la vitesse de relaxation de l'énergie potentielle. Ces deux paramètres sont évalués à partir d'éléments finis élasto-plastiques, dans le cas de composants sollicités thermiquement. Les résultats font état d'un accord satisfaisant entre les deux paramètres, bien queG apparaissent numériquement plus stable. Le paramètreJ* peut être sensible à des détails du maillage et à sa mise en charge.

     

A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto-plastic structures is constructed. A series of PQP formulae for contact problems and elastic-plastic structures is derived in the text, and some numerical examples are illustrated as well.     

An advanced finite element formulation for piezoelectric beam structures

Since many piezoelectric components are thin rod-like structures, a piezoelectric finite beam element can be utilized to analyse a wide range of piezoelectric devices effectively. The mechanical strains and the electric field are coupled by the constitutive relations. Finite element formulations using lower order functions to interpolate mechanical and electrical fields lead to unbalances within the numerical approximation. As a consequence incorrect computational results occur, especially for bending dominated problems. The present contribution proposes a concept to avoid these errors. Therefore, a mixed multi-field variational approach is introduced. The element employs the Timoshenko beam theory and considers strains throughout the width and the thickness enabling to directly use 3D constitutive relations. By means of several numerical examples it is shown that the element formulation allows to analyse piezoelectric beam structures for all typical load cases without parasitically affected results.     

A parallel method of eigenvalue analysis using dynamic substructuring and homotopy continuation

A parallel method to solve large eigenvalue problems using dynamic substructuring and homotopy continuation is presented. Unlike the conventional approaches in substructuring, the non-linear term is not neglected for improved accuracy. Therefore, instead of solving the approximated condensed problems, full exact condensed forms are treated. Homotopy continuation method is introduced to solve the non-linear reduced eigenvalue problem. In the process small number of substructure modes are used to reduce the original eigenvalue problem, and additional degrees of freedom, besides those at interfaces, are selected. The whole procedures are implemented to workstation cluster using PVM. To show how the method works, simple two-dimensional numerical examples are solved. It is demonstrated that the method yields highly accurate results and good parallel efficiency. © 1998 John Wiley & Sons, Ltd.     

A beam finite element for magneto-electro-elastic multilayered composite structures

A new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented. The element has six degrees of freedom represented by the displacement components and the cross-section rotation of its two nodes. The magneto-electric boundary conditions enter the discrete problem as work-equivalent forces and moments while the electro-magnetic state characterization constitutes a post-processing step. The element possesses the superconvergence property for the static problem of beams with uniform cross-section and homogenous material properties along the beam axis direction. Moreover, it is free from the shear locking phenomenon. The developed finite element is validated through comparison with plane-stress results for piezoelectric and magneto-electro-elastic structures. Last, applications for more complex magneto-electro-elastic systems are described.     

A higher-order finite element for analysis of composite laminated structures

A new six-node higher-order triangular composite layered shell finite element with six degrees of freedom at each node is presented. With respect to the inplane variables, the in-plane and the out-of-plane displacement fields of the element are quadratic and cubic respectively. By using Utku's method (AFFDL-TR-71-160, Air Force Third Conf., Wright Paterson, Ohio, 1971), the transverse shear strain energy is computed directly from the displacement field rather than from the stress couple field. Some typical bending problems for composite laminated beams and plates with different stack sequences are analyzed. Excellent agreements are obtained when compared to the exact solutions, the first order shear deformation theory (FSDT), the higher order shear deformation theory (HSDT) and some other existing finite element models. ‘Shear locking’ is avoided when the plate is thin.     

A finite element for the analysis of reinforced concrete structures

Formulation of a four-node isoparametric element suitable for modelling cracks in reinforced concrete structures is presented. The standard isoparametric element is known to give spurious shear stresses. The conventional remedy of selective integration breaks down in a ‘cracked’ element. It is shown that the proposed formulation gives superior results as compared to both the standard isoparametric element and the conventional selectively integrated element.