The specified boundary stiffness/force SBSF method for finite element subregion analysis

It is difficult to analyse a large, complex structure in sufficient detail to obtain accurate results everywhere. One approach is simply to refine the whole structure model in the regions of interest. Another approach is to identify a subregion of the structure and develop a separate refined model of the subregion. It is difficult to assure accuracy in this subregion model because of uncertainties in specifying boundary conditions and loading from the whole structure model solution. In the current literature, three methods other than whole model refinement have been described to deal with this problem. These are called the specified boundary displacement method, the linear constraint method and the zooming method. This paper describes a new approach to this problem of modelling subregions. This approach uses the stiffnesses and forces from the whole model solution at the nodes on the boundary of the sub-region model. Accurate displacement and stress solutions are obtained with this method as it takes into account the interaction between the new stiffness of the subregion and the rest of the structure. This approach is similar to substructuring; however, the equations outside the subregion are discarded rather than condensed out, which results in much less computation effort. Examples of the application of this method to the problem of a plate with a centre hole in tensile loading are presented. The results compared favourably with the results of the same problem solved using other methods, with significant improvement in accuracy over the specified boundary displacement method. Also presented are some results from design modification of the subregion which illustrate the potential of this method for redesign application.     

A fully automatic force method for the optimal shakedown design of frames

The paper presents a fully automatic way to handle the problem of the optimal shakedown design of planar frames. The evaluation of the elastic moments is essential for this design problem and due to the fact that they are design dependent, a classical iterative procedure is followed which updates these moments at the beginning of each iteration. A linear programming problem is then solved inside each iteration. The formulation adopted here is based on the force method which has computational advantages against the displacement method for this type of problems. Within the framework of the force method, the statical basis is provided by an easy to implement algorithm which selects a near minimal mesh basis for any planar graph. This basis is efficiently used, in a novel way, to find the flexibility matrix of the frame in a skyline form amenable to standard algorithms for its decomposition. The quickest way to the ground of each load is used to form the right hand side of the elastic compatibility equations for each load pattern. These equations are efficiently solved by standard back-substitution algorithms and the elastic bending moments to be introduced at the beginning of each iteration is established. Examples of application are also included.     

用于AGS结构分析的混合法

结合均匀化模型和加筋单元模型构造了一种混合模型用来分析复合材料格栅加筋板/壳结构（AGS）。所构造的加筋单元模型是一种高性能协调转角独立加筋板壳单元,保持了肋骨和蒙皮位移场的协调性,同时还满足肋骨和蒙皮具有独立转动条件,该单元中肋骨的方向和位置任意。混合法具有精度高、速度快等特点。通过典型算例讨论了肋骨间距和高度对均匀化模型计算结果精度的影响,通过对带孔复合材料AGS板孔边特殊点应力值的分析证明了混合法的有效性。      

A hybrid stiffness matrix for orthotropic sandwich plates with thick faces

A stiffness matrix is derived for a rectangular orthotropic sandwich plate element with thick faces by the assumed stress hybrid approach. It will be demonstrated that an independent polynomial can be used for the internal forces of the sandwich plate by the membrane theory (assumption of thin faces) and also for the additional moments and shear forces of the faces. The boundary displacements are approached solutions of the homogeneous differential equation of a sandwich beam.     

Vibration of frames and other structures with banded stiffness matrix

A general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi-storey building frames is outlined, and numerical results are presented for a simple test case and for a 19-storey frame.     

On the validity of the reduced bending stiffness method for laminated composite plate analysis

The ‘reduced bending stiffness’ (RBS) method has been used on occasions in the past as a means of simplifying the analysis of the flexural behavior of unsymmetrically laminated composite plates. However, the validity of the method has never been established. This paper makes direct comparisons between relatively simple, exact solutions for the static deflections, buckling loads and vibration frequencies of simply-supported plates and those arising from the RBS method. Extensive calculations are made for wide ranges of the physical parameters involved (aspect ratio, moduli ratio, lamination orientation angle, numbers of plies). The RBS method is found to yield sufficient accuracy for cross-ply plates, but errors up to 29% are obtained for angle-ply plates constructed with materials currently under development.     

基于动力刚度法的体外预应力梁自振频率分析

用预应力梁-杆组合结构模拟体外预应力梁,以体外预应力简支梁为例,建立了预应力梁杆单元动力刚度矩阵。采用动力刚度法,进一步推导出预应力梁-杆组合结构的整体动力刚度矩阵,利用Williams-Wittrick算法求解频率。本文以理论推导为基础,引入了动力刚度法。最后通过算例,讨论了各种因素对梁横向的振动特性的影响,并与试验值比较。计算结果表明:动力刚度法能够精确有效的求解体外预应力混凝土梁的横向振动问题。     

Non-linear vibration of frames by the incremental dynamic stiffness method

The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.     

A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis

A consistent tangent stiffness matrix for the analysis of non-linear contact problems is presented. The associated element has three or four nodes and establishes contact between three-dimensional structures like solids and shells. It accounts for the non-linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.     

A beam theory for thin-walled composite beams

A beam theory is presented that is formulated in terms of the in-plane elastic properties of the panels of the cross-section of a thin-walled composite beam. Shear deformation is accounted for by using a suitable form of the Timoshenko beam theory together with a modified form of the shear coefficient. The theory gives both the bending deflection and the shear deflection of a beam loaded by an applied transverse load. Numerical and graphical results obtained from a computer code show the effects of using different composite material systems and lay-ups in the panels of typical beams.     

变刚度碳纤维/环氧树脂复合材料薄壁圆管轴向压溃响应与破坏机制

通过控制缠绕线型改变轴管纤维角度,制备了一种轴向刚度渐变、压溃稳定的碳纤维增强树脂基复合材料(CFRP)变刚度薄壁圆管。对变刚度、[±45°]_n以及[90°]_n三类CFRP缠绕轴管进行轴向准静态压缩测试,结合数字图像相关技术(DIC)及有限元结果,对比三类结构压溃初始应变模式、损伤演化与应力状态结果,研究了变刚度结构的压溃响应与破坏机制。结果表明:不同纤维角度CFRP轴管因轴向刚度不同,压溃的初始破坏与损伤演化过程相异,三类结构产生不同的压溃响应与破坏模式。变刚度区连续变化的大角度纤维能有效地引发分层和"开花式"混合破坏,缓慢释放应变能,使变刚度CFRP轴管吸能效果明显优于其他两类结构。其峰值载荷为66.97 kN,压溃效率为50.8%,比吸能为10.1 kJ/kg,相对于[±45°]_n结构比吸能提升156.35%,压溃效率提升518.76%,相对于[90°])n结构比吸能提升16.9%,压溃效率降低27.3%。     

A mathematical programming method for the inelastic analysis of reinforced concrete frames

A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.     

复合材料副簧刚度的匹配设计方法

为了对复合材料副簧的刚度进行匹配设计,设计了包含有复合材料副簧的主副簧总成结构。采用集中载荷法计算复合材料副簧的等效载荷,根据原钢板弹簧的挠度变化来估算复合材料副簧的等效刚度。根据钢板弹簧设计理论,对复合材料副簧的等效刚度进行匹配设计。采用ABAQUS软件对设计的主副簧总成的总刚度进行有限元模拟,通过调整复合材料副簧的铺层数量来修正复合材料副簧的等效刚度。提出的匹配设计方法对复合材料板簧的推广应用具有重要意义。      

A fast multipole hybrid boundary node method for composite materials

This article presents a multi-domain fast multipole hybrid boundary node method for composite materials in 3D elasticity. The hybrid boundary node method (hybrid BNM) is a meshless method which only requires nodes constructed on the surface of a domain. The method is applied to 3D simulation of composite materials by a multi-domain solver and accelerated by the fast multipole method (FMM) in this paper. The preconditioned GMRES is employed to solve the final system equation and precondition techniques are discussed. The matrix–vector multiplication in each iteration is divided into smaller scale ones at the sub-domain level and then accelerated by FMM within individual sub-domains. The computed matrix–vector products at the sub-domain level are then combined according to the continuity conditions on the interfaces. The algorithm is implemented on a computer code written in C + +. Numerical results show that the technique is accurate and efficient.     

A new hybrid identification method for determining the material parameters of thin-walled tube under compressive stress state

Accurate and fast determination of material parameters of thin-walled tube under compressive stress state is essential for analyzing the compressive-type tube forming process. For the thin-walled tube with hollow structure, it is difficult to determine the material parameters directly from the experiment since buckling occurs easily when the tube suffers axial compressive loading. To accurately and rapidly identify the material parameters of thin-walled tube under compressive stress state, a hybrid inverse identification method is proposed based on tube lateral compression test with combining finite element simulation, regression analysis and genetic algorithm. By employing the proposed method, the Swift law hardening parameters of thin-walled tubes with different materials and specifications under compressive stress state are identified. Furthermore, the efficiency and accuracy of the proposed method are discussed in comparison with the previous researches. The results show that: (1) for 6061-T4 and 1Cr18Ni9Ti tubes, the maximum relative predicting errors of forces in tube lateral compression using the identified material parameters are less than 9%; (2) for aluminum tube ∅100 × 2 (diameter × thickness, mm), the maximum discrepancies between the simulated and experimental circumferential strains are less than 0.0274 for 30–70% reductions, and the simulated tube profiles deviate from the experiment less than 10% at reductions of 0–78%; and (3) the proposed method almost saves 80% computational time compared with the previous stepwise optimization method.     

A computationally efficient method for the limit elasto plastic analysis of space frames

A computationally efficient method for the first order step-by-step limit analysis of space frames is presented. The incremental non-holonomic analysis is based on the generalized plastic node method. The non-linear yield surface is approximated by a multi-faceted surface, thus avoiding the iterative formulation at each load step. In order to prevent the occurrence of very small load steps a second internal and homothetic to the initial yield surface is implemented which creates a plastic zone for the activation of the plastic modes. This implementation reduces substantially the computational effort of the procedure without affecting the value of the final load. The solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. The application of the conjugate gradient method is based on some recent developments on improved matrix handling techniques and efficient preconditioning strategies. A number of test problems have been performed which show the usefulness of the proposed approach and its superiority in respect to efficient direct methods of solution in both storage requirements and computing time.     

双闭室复合材料薄壁梁的结构阻尼细观分析

研究双闭室复合材料薄壁梁的结构阻尼特性。基于单层混杂材料的细观力学阻尼计算方法和多胞模型,分别获得单层复合材料的等效阻尼特性和等效弹性特性;基于变分渐进法（VAM)和Hamilton原理,建立双闭室复合材料薄壁梁振动方程;采用Galerkin法对薄壁梁进行自由振动分析;在获得薄壁梁振动模态矢量的基础上,根据最大应变能理论,对薄壁梁的模态阻尼性能进行预测,并且将阻尼预测的结果与现有的有限元计算结果进行对比,验证了本文阻尼分析模型的有效性。进一步针对四种种构型双闭室复合材料薄壁箱形梁,进行阻尼计算,揭示了纤维铺层角和纤维含量的影响。     

A health management algorithm for composite train carbody based on FEM/FBG hybrid method

In this study, a health management program for a composite train carbody was developed using the acquired strain distributions from fiber Bragg grating (FBG) sensor arrays. To determine appropriate locations for the FBG sensors, a finite element analysis (FEA) was executed. In this FEA, a FE model of the Korean tilting train (TTX) was used as a representative composite carbody train. The FEA results of various derailment situations and high speed operation on curved track were used as the database of each deformation case. In the last step, the health management program was produced using LabVIEW software. In this post-processing algorithm, the method of least squares was used to determine the difference between the FEA results and the acquired strains. This program shows the estimated deformations and plots of the acquired strains, as well as displaying an emergency indicator when necessary, all through post-processing of the strains. Finally, this FEM/FBG hybrid method was verified by several simulations using the reproductive sensor data.     

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

 A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a three-dimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P−Δ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. Received: 2 May 2000 / Accepted: 15 July 2002