Updating the Craig–Bampton reduction basis for efficient structural reanalysis

A Combined Approximation (CA) based reanalysis technique is proposed for updating the static modes in a reduction basis which can be used for sizing optimization problems. Although the proposed technique is utilized under the framework of the Craig–Bampton (CB) method, it can be employed with any condensation procedure that involves the computation of the static modes. An automated update scheme is also presented that switches the proposed technique with the exact analysis when the computational efficiency is lost. Moreover, the Enriched Craig–Bampton (ECB) method is studied for the reanalysis of the normal modes. The ECB‐ and the CA‐based techniques are merged for efficient update of the CB reduction basis. An academic test problem is utilized for the demonstration of the introduced concepts. Copyright © 2010 John Wiley & Sons, Ltd.     

用步进电机实现连续变焦距光学镜头的变焦控制

根据望远镜的工作原理，对变焦距光学镜头的变焦运动进行了定性分析，并且根据理想光学系统的物像关系式推导出该镜头运动镜组的运动方程。该连续变焦控制的实验装置包括步进电机，电机驱动器以及控制平台，其控制程序用VisualC 编写。实验表明，该方法能方便地实现连续变焦距光学镜头的变焦控制。     

Thin-lens Theory of Zoom Systems

The Gaussian design of optically compensated zoom systems is described and the procedure is applied to the three-lens and four-lens systems. A method for the control of the primary aberrations of thin lens zoom systems during zooming is described, which involves the solution of sets of simultaneous quadratic equations by a damped least squares technique. Examples are given of the procedure when applied to the previously designed three and four-lens optically compensated systems. Finally the method is applied to the design of a thin lens triplet with specified values of the primary aberrations, for use in conjunction with the above mentioned zoom systems.     

Nonlinear thermal analysis with a boundary element zone condensation technique

This paper presents a substantially more economical technique for the boundary element analysis (BEA) of a large class of nonlinear heat transfer problems including those with temperature dependent conductivity, temperature dependent convection coefficients, and radiation boundary conditions. The technique involves an exact static condensation of boundary element zones in a multi-zone boundary element model. The condensed boundary element zone contributions to be overall sparse blocked boundary element system matrices are formed once in the first step of the iterative nonlinear solution process and subsequently reused as the nonlinear parts of the overall problem are evolved to a convergent solution. Through a series of example problems it is demonstrated that the zone condensation technique facilitates the use of highly convergent iterative strategies for the solution of the nonlinear heat transfer problem involving modification and subsequent factorization of the overall boundary element system left had side matrix. For heat transfer problems with localized nonlinear effects, the condensation technique is shown to allow for the solution of nonlinear problems in less than half the CPU time required by methods that do not employ condensation.     

Zoom lens design for a novel imaging spectrometer that controls spatial and spectral resolution individually

A novel imaging spectrometer can individually control spatial and spectral resolution by using zoom lenses as the foreoptics of the system and a focusing lens. By varying the focal length we can use the focusing lens to change the spatial and spectral dimensions; with the foreoptics, however, we can change only the spatial dimension. Therefore the spectral resolution and the spectral range are affected by the zoom ratio of the focusing lens, whereas the spatial resolution and the field of view are affected by the multiplication of the zoom ratios of the foreoptics and the focusing lens. By properly combining two zoom ratios, we can control the spectral resolution with a fixed spatial resolution or the spatial resolution with a fixed spectral resolution. For an imaging spectrometer with this novel zooming function, we used the lens module method and third-order aberration theory to design an initial four-group zoom system with an external entrance pupil for the focusing lens. Furthermore, using the optical design software CODE V, we obtained an optimized zoom lens with a focal-length range of 50 to 150 mm. Finally, the zoom system with its transmission grating in the Littrow configuration performs satisfactorily as the focusing lens of an imaging spectrometer in the wavelength range 450-900 nm.     

基于ZEMAX二组运动变焦系统凸轮曲线优化

凸轮曲线优化是机械补偿变焦距光学系统后期设计的一个重要环节.只有沿着准确的凸轮曲线控制变焦距系统的活动组份,才能保证有稳定良好的像质.本丈提出一种基于ZEMAX的凸轮曲线优化设计新方法.该方法利用ZEMAX宏语言编写变焦距系统凸轮曲线设计程序,得到变倍组和补偿组之间准确的相对位移关系.同时,该程序能够计算出随着光学系统焦距变化的像斑尺寸连续变化曲线,实现在设计凸轮曲线的同时,随着焦距的连续变化,实时了解光学系统综合像质走向.此举对凸轮曲线的合理性提供了至关重要的佐证.     

An exact reanalysis algorithm using incremental Cholesky factorization and its application to crack growth modeling

In this paper, an exact reanalysis algorithm based on an incremental Cholesky factorization is presented, which can solve a linear system of equations when a small portion of the coefficient matrix is modified. The efficiency of the proposed algorithm is demonstrated by modeling quasi‐static crack growth in the extended finite element method. The example presented shows that a 60% to 70% reduction in computational time is achievable by using the reanalysis approach for solving crack growth problems. It is shown that the reanalysis approach has increasing benefits as the mesh density increases. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of superheated steam on non-equilibrium condensation in ejector primary nozzle

In order to reduce the non-equilibrium condensation occurring in ejector primary nozzle, wet steam model was adopted to investigate the relationship between steam superheated level and non-equilibrium condensation within ejector primary nozzle. Simulation data of axial static pressure along primary nozzles were validated with experimental data reported in literature. The non-equilibrium condensation process from homogeneous nucleation to droplet growth stage and the resulting products were carefully studied. Moreover, six inlet superheated levels from 5 K to 30 K with the increment of 5 K were compared, and simulation results showed that the increase of superheated level from 5 K to 30 K causes 40.22% delay in the location and 43.92% reduction in the intensity of the condensation shock. Furthermore, there is about 24.30% liquid mass fraction decrease when the superheated level raises to 30 K and total entropy generation increases slowly with the increase of superheated level.     

Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas

Several exact fast static structural reanalysis techniques, introduced by researchers mostly for truss structures and some for frames and plate structures, are reviewed. Most utilize the property that the solution of a system of linear equations can be updated inexpensively when the matrix is changed by a low‐rank increment. This paper shows that these methods are variants of the well‐known Sherman–Morrison and Woodbury (SMW) formulas for the update of the inverse of a matrix. In addition, the paper extends the low‐cost linear reanalysis in the spirit of the SMW formulas to some non‐linear reanalysis problems. For a linear reanalysis, the extension reduces to the SMW formulas. Copyright © 2001 John Wiley & Sons, Ltd.     

Paraxial analysis of mechanically compensated zoom lenses. 3: Five-component type

With the help of Gaussian Brackets, this paper presents a paraxial study of the mechanically compensated zoom lens which consists of a fixed front component, three independently movable components, and a fixed fifth component. The expressions, which define the displacement of components at zooming, the critical point of displacement, and the singular point of displacement are derived. Some numerical examples of the zooming locus are given.     

Primary aberration changes produced by arbitrary movements of paraxial rays

A general algorithm is proposed for evaluating variations of primary monochromatic and chromatic aberrations of single surface or thin-lens components when the paraxial marginal and chief rays are arbitrarily moved. Compared to the earlier algorithm, optical invariants of the original and the new optical configurations could be different, which is common when the object distances are changed or for zoom lenses with different f-numbers on zooming. According to the positions of object and pupil, four special cases arise which lead to the need for four separate sets of coefficients, and a new parameter which is always determinate is used to indicate which set is to be chosen.     

Inverse Sub‐Structuring Theory for Coupled Product Transport System Based On the Dummy Masses Method

It is of high importance to predict the components frequency response functions (FRFs) for obtaining the coupled product transport system's response. However, the components behaves much differently when coupled with another components compared with that in free state. Inverse sub‐structuring method has been recently proposed and applied for inverse analysis of the dynamical response of coupled product transport system. The component‐level FRFs and the coupling dynamic stiffness are all predicted from only the system‐level FRFs, facilitating the engineering design for product transport system. However, in most engineering application practices, the system‐level FRFs from coupling degrees of freedom may not be measured accurately because of the difficulties of vibration excitation and/or response measurement for the coupled interface between components within the limited accessible space. The aim of this paper is to develop a new FRF‐based indirect inverse sub‐structuring method for the analysis of the dynamic characteristics of a two‐component coupled product transport system without measuring system‐level FRFs at the coupling degrees of freedom. A so‐called dummy masses method is developed and applied for predicting the unmeasured FRFs at the coupling degrees of freedom, and the inverse sub‐structuring approach based on the dummy mass method is derived for inverse analysis of coupled product transport system, which is further verified by a lumped‐mass model, showing exact agreement. Finally, the experiment on a physical prototype of two‐substructure coupled product transport system is performed to further check the accuracy of the suggested method. The new method shows its great application prospect in coupled product transport system.     

Reanalysis procedure for large structural systems

An efficient procedure is presented for repetitive analysis of structures, with large numbers of degrees of freedom and design variables, as they are progressively modified during the automated optimum design process. The three key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the governing finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov-Galerkin technique. The reanalysis procedure is applied to the linear static and free vibration problems of framed structures. Changes in both the sizing and shape (configuration) design variables are considered. For static problems the similarities between the proposed procedure and the preconditioned conjugate gradient technique are identified and are exploited to provide a physical meaning for the preconditioned residual vectors. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.     

EXACT MODAL SYNTHESIS TECHNIQUES USING RESIDUAL CONSTRAINT MODES

A new exact modal synthesis method for finding natural frequencies and modes of structures is proposed, in which the exact residual constraint modes based upon an incomplete set of normal modes of substructures with fixed interfaces are expressed in two parts. These are the static constraint modes and a residual term with which it represents exactly the effect of normal modes not retained. The modal synthesis uses a Ritz procedure and an iterative technique is presented for solving the non-linear equations of modal synthesis. This has the advantage that the results given by its first iteration are exactly those given by the Craig–Bampton–Hurty modal synthesis method, which leads to rapid convergence of subsequent iterations. The proposed method is an improvement of Hu's exact modal synthesis method and is also shown to have as its limit the method of exact dynamic condensation. Numerical examples show that using the proposed method yields superior accuracy when only a few lower modes are used. © 1997 by John Wiley & Sons, Ltd.     

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

This paper investigates the free vibration characteristics of a beam carrying multiple two‐degree‐of‐freedom (two‐dof) spring–mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring–mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two‐dof spring–mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two‐dof spring–mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two‐dof spring–mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two‐dof spring–mass systems attached to the beam. Furthermore, if the total number of two‐dof spring–mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter. Copyright © 2005 John Wiley & Sons, Ltd.     

ON THE AUTOMATIC SELECTION OF REANALYSIS TECHNIQUES IN MACHINE TOOL STRUCTURAL ELEMENT OPTIMIZATION

Structural reanalysis technique methods are employed in structural optimization to analyze new designs efficiently using previous information. In this paper, an algorithm is developed to automatically select proper reanalysis techniques for efficient and accurate analysis during the machine tool structural element optimization process. This algorithm provides an error estimator to control the solution accuracy and a reanalysis capability to eliminate the problem dependency of using a single reanalysis technique. An example is used to demonstrate the advantage of this algorithm over the complete (exact) analysis or single reanalysis technique.     

刚度局部更改的一种通用精确算法

本文研究结构局部刚度改变时的结构重分析方法。结构局部刚度改变问题在结构有限元计算时常会遇到,例如:结构物个别构件的破坏或损伤、构件的局部屈服等等。本文推导了一种新的算法,利用原结构刚度矩阵的LDLT分解因子,通过代数运算获得新结构的解。该算法的结果是精确且通用的,不仅可用于杆系结构也可用于连续体,而计算量与目前已有的各种专用近似方法相同。算例表明,新方法是有效的。     

A preconditioned conjugate gradient approach to structural reanalysis for general layout modifications

This paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications. It is suitable for all types of layout modifications, including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently. The approach is based on the preconditioned conjugate gradient technique. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that the condition number of the preconditioned matrix is remarkably reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

基于降阶模型的非经典阻尼结构拓扑修改的复模态重分析方法

摘要：对非经典阻尼结构自由度增加的拓扑修改重分析问题,提出了一种近似方法。这一方法基于初始结构和拓扑修改结构的降阶模型,采用动力缩聚和复矩阵奇异值分解两个步骤,然后结合瑞利商逆迭代法来求解。数值算例结果表明：该方法具有较高的精度,且效率高。     

多级齿轮传动转子系统的模态缩减与振动特性分析

提出了一种适用于多级齿轮传动转子系统的模态缩减法,以某透平驱动水泵系统为研究对象,采用有限元法建立了系统的动力学模型,并利用模态缩减法减少了系统自由度.在此基础上研究了系统的固有特性、不平衡量与静态传递误差引起的稳态响应、启动状态下的瞬态响应以及稳定运转下突加不平衡时的瞬态响应.结果表明,在计算系统的固有频率和稳态响应...