Structural Reanalysis Research Articles

감도계수 반복법을 이용한 비비례감쇠계의 고유치 및 고유벡터 변화량 해석

This study predicts the modified eigenvectors and eigenvalues of the non-proportional damped structure due to the change in the mass, damping and stiffness of structure by iterative method of the sensitivity coefficient using the original dynamic characteristic. The method is applied to the non-proportional damped 3 degree of freedom system by modifying the mass, damping and stiffness. The predicted dynamic characteristics are showed a good agreement with these from the structural reanalysis using the modified mass, damping and stiffness.

Accelerated engineering design optimization using successive matrix inversion method

In a design optimization procedure, many repeated system analyses are conducted to evaluate certain performances of successively modified structural designs. To alleviate the high computational cost of structural reanalysis, an augmented preconditioner is introduced by using the successive matrix inversion (SMI) method. The SMI method, as an exact matrix solver, is successively applied to an iterative procedure to accelerate the solution convergence by improving the numerical condition of the reanalysis system. In this work, a new iterative technique, the binomial series iterative (BSI) method, is developed from the binomial series expansion by using the same concept as SMI. As a combined iterative (CI) method, SMI is incorporated in the procedure of BSI. The CI method, combined with SMI, shows sufficient efficiency and robustness through a stable iterative behaviour due to simple and straightforward computations in the iterative procedure. Published in 2005 by John Wiley & Sons, Ltd.

설계파라미터 변경에 의한 비례 감쇠구조물의 동특성 변화 해석

An efficient method for change of eigenvectors and eigenvalues due to the modifying proportional damping structure using sensitivity coefficients is presented. Sensitivity coefficients are determined by iteration with eigenvalue and eigenvectors before modification of system. The proposed method is applied to examples of 3 degrees of freedom system and plate by modifying mass and stiffness. The predicted change of eigenvectors and eigenvalues are in a good agreement with these from the structural re-analysis after modification of mass and stiffness.

Nonlinear dynamic reanalysis of structures by combined approximations

A major difficulty in non-linear dynamic reanalysis by mode superposition is the need to repeat the eigenproblem solutions. This study shows how the combined approximations approach can be used to overcome this difficulty. The approach is based on the integration of several concepts and methods, including matrix factorization, series expansion and reduced basis. The advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure. In the procedure developed for material non-linearity, improved basis vectors are introduced using the concepts of Gram–Schmidt orthogonalizations and shifts. Numerical examples show that accurate approximations are achieved efficiently for very large changes in the design variables.

Nonlinear Perturbation Theory for Structural Dynamic Systems

A novel nonlinear perturbation theory for structural dynamic systems is developed that can provide an exact relationship between the perturbation of structural parameters and the perturbation of modal parameters. A system of governing equations based on the developed theory is further derived, which can be utilized for general applications, such as structural reanalyses, eigendata modification, model updating, and damage identification, suitable for all types of structures including mechanical systems, framed structures, and continua. Neither model reduction nor mode shape expansion is required for modal updating and damage identification because information about incomplete measured modal data can be directly employed. The developed theory successfully avoids adopting a Taylor series expansion procedure and then the derivatives of modal parameters are not required. Computational procedures based on the derived nonlinear governing equations are presented for eigendata modification, model updating, and damage identification. The Jacobi transformation method and the accelerated modal method are introduced to make the proposed techniques particularly suitable for cases with a very large perturbation of structural parameters. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed techniques. The results show that the modified modal parameters can be predicted exactly even for cases with a large modification of structural parameters, and the analytical model can be adjusted correctly using the information about limited modal data available.

Static reanalysis of structures with added degrees of freedom

AbstractThis paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate‐gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd.

Error evaluation in approximate reanalysis of structures

It was found in previous studies that the combined approximations (CA) approach developed recently provides accurate results in approximate reanalysis of structures. In this study it is first shown that nonlinear reanalysis and eigenproblem reanalysis can be formulated as a linear reanalysis problem. Then, the convergence behaviour of approximate linear and eigenproblem reanalysis is investigated, and expressions for error evaluation are developed. Some numerical examples show that small errors in the response are obtained for very large changes in the design variables by low-order approximations. The errors evaluated by the expressions developed are similar to the true errors. It was found that lower and upper bounds introduced by the CA method provide good estimation of the exact eigenvalues.

Successive Matrix Inversion Method for Reanalysis of Engineering Structural Systems

Over the past several decades, numerous structural analysis techniques have been developed to represent physical systems behavior more realistically, and the structural models, therefore, have become larger and more complex. Even though modern computer power has increased significantly, cost of computational analysis has been a major restrictive factor in a structural system design involving multiple disciplines and repetitive simulations. A new reanalysis technique is developed. The successive matrix inversion (SMI) method is most suitable for reanalysis of structures. The SMI method reproduces exact solutions for any localized modification of the initial system. Several numerical examples are given to demonstrate the efficiency of this method.

Procedures for approximate eigenproblem reanalysis of structures

AbstractIn vibration mode superposition analysis, the main computational effort is spent in the solution of the eigenproblem. In reanalysis procedures this solution must be repeated for each change in the design. It is shown in this study how the combined approximations method can be used to improve the efficiency of some common iterative procedures. These procedures can then be used for efficient eigenproblem reanalysis. Solution of the reduced eigenproblem by the combined approximations method is first demonstrated. Procedures based on inverse iteration, inverse iteration with shifts, and subspace iteration are then considered. Some numerical examples show that high accuracy is achieved for very large changes in the design. In cases where higher accuracy is required, additional terms of the approximations may be considered. Copyright © 2004 John Wiley & Sons, Ltd.

A finite element algorithm for reanalysis of structures with added degrees of freedom

This paper is focused on the reanalysis of structures with added degrees of freedom. By suitably partitioning the extended stiffness matrix, we present a preconditioned conjugate gradient algorithm to analyze the modified structure. The algorithm preserves the ease of implementation and improves significantly the quality of results. In particular, the algorithm can adaptively monitor the accuracy of approximate solutions. It is applicable to general finite element systems. The computational cost is significantly reduced. Numerical examples are given to show the effectiveness of the presented reanalysis algorithm.

The implementation of a vector-valued rational approximate method in structural reanalysis problems

An efficient implementation of a vector-valued rational approximation in structural reanalysis problems is presented. The implementation is based on combining the power series expansion with a rational approximation. The main objectives are (1) to preserve the ease of implementation of the local approximation and (2) to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometrical changes and elimination of members. The method is suitable for different types of structures, such as trusses, frames, grillages, etc. The computational cost is significantly reduced. Numerical examples have shown that excellent results can be achieved for very large changes in cross-sections and in structural geometry.

Against repair-based reanalysis in sentence comprehension.

Structural reanalysis is generally assumed to be representation-preserving, whereby the initial analysis is manipulated or repaired to arrive at a new structure. This paper contends that the theoretical and empirical basis for such approaches is weak. A conceptually simpler alternative is that the processor reprocesses (some portion of) the input using just those structure-building operations available in first-pass parsing. This reprocessing is a necessary component of any realistic processing model. By contrast, the structural revisions required for second-pass repair are more powerful than warranted by the abilities of the first-pass parser. This paper also reviews experimental evidence for repair presented by Sturt, Pickering, and Crocker (1999). We demonstrate that the Sturt et. al. findings are consistent with a reprocessing account and present a self-paced reading experiment intended to tease apart the repair and reprocessing accounts. The results support a reprocessing interpretation of Sturt et. al.'s data, rendering a repair-based explanation superfluous.

Structural modal reanalysis for topological modifications with extended Kirsch method

In this paper, a new effective method for modal reanalysis of structures subjected to topological modifications is presented. The effect of inertia coupling between the old degrees of freedom and the new added degrees of freedom is introduced with iterative perturbation. Furthermore, the extended Kirsch method is utilized to improve the accuracy of the starting solutions. The numerical examples are given for frame and truss structures. Results are compared to the exact solution and prove that the proposed method is effective.

Feeding in Atractaspis (Serpentes: Atractaspididae): a study in conflicting functional constraints

African fossorial colubroid snakes of the genus Atractaspis have relatively long fangs on short maxillae, a gap separating the pterygoid and palatine bones, a toothless pterygoid, and a snout tightly attached to the rest of the skull. They envenomate prey with a unilateral backward stab of one fang projected from a closed mouth. We combined structural reanalysis of the feeding apparatus, video records of prey envenomation and transport, and manipulations of live and dead Atractaspis to determine how structure relates to function in this unusual genus of snakes. Unilateral fang use in Atractaspis is similar to unilateral slashing envenomation by some rear-fanged snakes, but Atractaspis show no maxillary movement during prey transport. Loss of pterygoid teeth and maxillary movement during transport resulted in the inability to perform. 'pterygoid walk' prey transport. Atractaspis transport prey through the oral cavity using movement cycles in which mandibular adduction, anterior trunk compression, and ventral flexion of the head alternate with mandibular abduction and extension of head and anterior trunk over the prey. Inefficiencies in manipulation and early transport of prey are offset by adaptability of the envenomating system to various prey types in both enclosed and open spaces and by selection of prey that occupy burrows or tunnels in soil. Atractaspis appears to represent the evolutionary endpoint of a functional conflict between envenomation and transport in which a rear-fanged envenomating system has been optimized at the expense of most, if not all, palatomaxillary transport function.

Reanalysis of linear and nonlinear structures using iterated Shanks transformation

Reanalysis of structures is a common task in two important fields of structural engineering, namely optimization and reliability. It implies the solution of the kinematic equations for each new set of data. In order to simplify this task several approximate methods have been developed. In this paper a simple method for reanalysis, applicable to either linear or nonlinear structures, is proposed. It is based on the improvement of the Neumann resolvent series, which diverges beyond a certain radius, by means of the iterated Shanks transformation. The method is compared with two relevant proposals intended to improve the convergence of the Neumann series, namely the Padé series and the scaled approximation methods. The accuracy and simplicity of the proposed method is demonstrated through some examples concerning linear and nonlinear structures.

Accurate reanalysis of structures by a preconditioned conjugate gradient method

AbstractA preconditioned conjugate gradient (PCG) method that is most suitable for reanalysis of structures is developed. The method presented provides accurate results efficiently. It is easy to implement and can be used in a wide range of applications, including non‐linear analysis and eigenvalue problems. It is shown that the PCG method presented and the combined approximations (CA) method developed recently provide theoretically identical results. Consequently, available results from one method can be applied to the other method. Effective solution procedures developed for the CA method can be used for the PCG method, and various criteria and error bounds developed for conjugate gradient methods can be used for the CA method. Numerical examples show that the condition number of the selected preconditioned matrix is much smaller than the condition number of the original matrix. This property explains the fast convergence and accurate results achieved by the method. Copyright © 2002 John Wiley & Sons, Ltd.

Structural Reanalysis using a Neural Network-based Iterative Method

Structural design requires a knowledge of the displacements and stress resultants occurring in a structure so that the designer can be satisfied that all functional requirements and design constraints are met. It is usual to base the first analysis on an initial design and then review the design constraints and make any desirable changes in the design data. If we continue this process we encounter a circular operation of repeated design and analysis. The process is handicapped by the dissimilar computational natures of analysis and design making integration difficult. A neural network type of computational device is suitable for continuous updating of the analysis with provision for a wide range of structural design modifications including those affecting geometry, topology, nodes, loads, supports, and material properties. The convenience in reanalysis introduced will generally require more memory in the computer and faster processing compared with the conventional approach. The practicality of the method...

Static reanalysis of discrete elastic structures with reflexive inverse

This paper presents a direct method for the static reanalysis of structures. We use the concept of the reflexive inverse in the sense of Moore–Penrose generalized inverse to express a general solution of discrete systems without any boundary condition. We use a simple decomposition of the stiffness matrix to avoid its inversion. We give a comparison of the processing time of this method with the duration of a complete analysis with finite elements. The reanalysis of the stiffness is based on the mixed conditions linking displacements and related efforts. In the second part we concentrate on this reanalysis and we give as an application the reanalysis of the geometry and the reanalysis for mesh refining. This method is general, enabling the reanalysis of structures with variation of the boundary conditions in loading and displacement. It also enables reanalysis of the structural stiffness and makes it possible to add or remove structural elements. It can easily be applied to the study of nonlinear behavior (case of damaging, plasticity, nonlinear elasticity…).

A scheme for engineer-driven mechanical design improvement

The role of stress analysis in design is limited by the batch processing of single design geometries when subjected to prescribed load cases. While this approach is reasonable for detailed design, it limits the engineer in early stage design, when the rapid availability of stress information for a wide range of candidate design geometries is perhaps more important than geometric precision. This paper presents structural re-analysis in a boundary element context, providing information on a suitable object-oriented structure and introducing the operations required when processing various types of re-analysis in both (two-dimensional) 2D and more recent developments in (three-dimensional) 3D simulation. Computational performance improvements (over a full analysis) of up to 80% are found in both 2D and 3D, depending on the degree of perturbation to a pre-existing boundary element method model and other factors discussed. Illustrations from an industrial setting show how stress reduction and weight reduction may be achieved as analysis results guide the design in the concept stage.

An adaptive iteration algorithm for structural modal reanalysis of topological modifications

AbstractAn adaptive iteration algorithm is presented in this paper for structural modal reanalysis of topological modifications. The rules of adaptation are given. The method is based on matrix perturbation and can be implemented easily on the computer. A little computation effort is involved, which is very important for topological modification with the increase of the joints and the number of degrees of freedom. In order to illustrate the method, three examples are given. The results show that the proposed method is effective for structural modal reanalysis of topological modifications. Copyright © 2002 John Wiley & Sons, Ltd.