General analysis and application to redundant arches under static loading

The aim of this paper is to define an exact formulation of a curved beam finite element for static analysis. The basic equations are combined in the coupled fundamental system in terms of radial displacement v, tangential displacement u and rotation ϕ. An original procedure for solving the fundamental system of equations is used. A finite element formulation based on shape functions that satisfy the homogeneous form of the fundamental system of differential equations is developed. The effects of bending moment, axial extension and transverse shear are taken into account. The exact elastic solution renders the element obtained free of shear and membrane locking.An efficient numerical procedure is presented for determining the pressure curve in the case of circular arches under static loading and arbitrary bonding conditions. The solution obtained is applicable to the analysis of both thin and thick curved beams.Several examples of arches with various loading and boundary conditions are investigated to illustrate the validity and the accuracy of the method. Finally, the effect of the arch rise on the structural response is pointed out.     

弹性地基中三维动力问题的耦合粘性边界

根据波在地基的3个方向(x、y、z轴)都可以进行传播的特点,假定了地基中质点沿3个方向的振动表达式,通过胡克定律和波动理论,推导了弹性地基中三维动力问题的耦合粘性边界的公式。数值计算结果与理论精确解的比较表明:有限区域的有限元与截断边界的耦合粘性边界结合,能够较准确地求解弹性半空间的三维波动问题。本文耦合粘性边界是和频率无关的,可以适用于频域和时域的计算。     

索结构找形分析的精确单元方法

索找形问题是索结构分析中所要解决的首要问题,在给定边界条件下,所施加的预张力和外部荷载通过调节索的 形状来平衡。本文研究索结构初始形状确定的精确有限单元法,对于常见的荷载形式,构造了线性和非线性两大类共5种 单元,适用于一般的索结构找形计算,并且可以给出精确的解答。本文通过将水平方向和竖直方向的平衡方程解藕,得出 了索单元的精确描述格式,并保证了索结构形状的唯一性。文中以索结构内部结点坐标作为基本未知量,以结点平衡方程 为基本方程,通过直接求解单元的平衡微分方程得到单元刚度矩阵的解析表达式。对于由线性单元组成的索结构,其基本 方程为线性,可直接求解;对于含有非线性单元的索结构,其基本方程为非线性,需通过迭代求解,文中构造了相应的 Newton法迭代格式。本文方法所需单元数目少,计算量小,所得到的解答为数值精确解。数值算例表明本法稳定可靠。     

A new approach to stability analysis of frame structures using Trefftz-type elements

This paper presents some new developments in structural stability analysis. A novel Trefftz-type finite element and efficient algorithms are proposed for calculating numerically exact solutions for frame structures. New shape functions are constructed by using general solutions of the homogeneous governing equation and an exact Trefftz element is formulated. An iterative algorithm based on conventional eigenvalue extraction method is then proposed, with which very accurate solutions can be obtained efficiently by using coarse finite element meshes. Further, an efficient method based on the new element matrices and Rayleigh's quotient is developed for a posteriori error estimation and solution improvement. Numerical examples are presented to demonstrate the effectiveness of the proposed element and algorithms. Finally, concluding remarks are made including those on the further extension of the approach.     

三维切槽孔爆破的数值分析

本文利用大型 ADINA有限元程序对三维切槽孔、二维切槽孔和圆形孔爆破作了线弹性数值分析 ,结果表明三维槽孔爆破具有应力高度集中现象、应力的空间分布可以人为控制、切槽效应小于二维切槽孔爆破 ,遵守能量守恒规律。这说明三维切槽孔爆破方法能够应用于破岩爆破 ,其效率明显高于传统的圆孔爆破方法。     

边界元法解各向异性应力集中问题

针对各向异性板的应力集中问题,以复变函数表达的基本解作为权函数建立了边界元法格式,给出了含圆孔的各向异性板应力集中问题的数值算例,通过数值结果与有限元方法的比较可知：边界元法对于各向异性板应力集中问题的求解具有较高的计算精度和广泛的适应性。     

多层地基上相邻基础动力相互作用求解

对于基础-地基-基础动力相互作用(FSFI)问题的求解,以往只是针对半无限均质或者单层地基来进行求解。利用改进的比例边界有限元方法(SBFEM)与有限元方法(FEM)相结合来求解多层地基之上的FSFI问题,SBFEM求解时计算空间域降低一维,并且不需要边界元所要求的基本解。针对典型算例对上述数值方法进行具体的验证,并就多层地基上FSFI问题进行求解。计算结果表明,所提出的数值算法在求解多层地基之上的FSFI问题有广泛的适用性,并且有较好的求解精度。     

A new rectangular finite element based on the strain approach for plate bending

This work deals with the development of a new four nodes rectangular finite element for the linear analysis of plate bending with transverse shear effect. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. The element possesses three essential external degrees of freedom at each of the four corner nodes and satisfies the exact representation of the rigid body modes of displacements. This element is found to be numerically more efficient than the corresponding displacement-based element and its precision is evaluated through a series of tests cases related to thick and thin plates.     

Exact solutions for thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment

The exact solutions for torsional analysis of thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment are presented for the first time. For this, a general thin-walled composite beam theory with arbitrary lamination is developed by introducing Vlasov's assumption and the equilibrium equations and the force–deformation relations are derived from the energy principle. Applying the displacement state vector consisting of 14 displacement parameters and the nodal displacements at both ends of the beam, the displacement functions are derived exactly. Then, the exact stiffness matrix for torsional analysis is determined using the force–deformation relations. As a special case, the closed-form solutions for symmetrically laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the closed-form solutions and the finite element results using the Hermitian beam elements and ABAQUS's shell elements.     

Reliability analysis of tunnels using a metamodeling technique based on augmented radial basis functions

Metamodeling techniques have been developed and used for years in engineering reliability analysis involving expensive response simulations. In practical tunnel engineering problems where finite element (FE) simulations are required, the limited state/performance functions are in general implicit and nonlinear, and it is difficult to apply traditional gradient-based or sampling-based reliability methods, especially for large-scale problems. There is a need to develop accurate and efficient metamodels for practical tunnel engineering applications. In this paper, a metamodeling technique for reliability analysis of tunnels was studied based on augmented radial basis functions (RBFs). With a relatively small size of samples, the RBFs were used to create accurate approximate functions for different types of responses including linear and higher-order nonlinear functions. With the RBF-based metamodel constructed to express a limit state/performance function, Monte Carlo simulations (MCS) were applied to evaluate failure probability. The failure probability and reliability index obtained using the RBF-based metamodeling method were found to have good accuracy with a reasonable number of sample points. The reliability analyses of two existing tunnel examples showed that the augmented RBF metamodeling approach was efficient and effective for tunnel engineering problems.     

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

The seismic analysis of a viscoelastic half-space under two-dimensional (2D) oblique incident waves is carried out by the finite/infinite element method (FIEM). First, the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves. With the present formulation, no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear, while no critical angle exists for P waves. Next, the equivalent seismic forces of the earthquake (Taft Earthquake 1952) imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum. Based on the asymmetric finite/infinite element model, the frequency-domain motion equations for seismic analysis are presented with the key parameters selected. The results obtained in frequency and time domain are verified against those of Wolf’s, Luco and de Barros’ and for inversely computed ground motions. The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles, but not for under-critical incident angles. Other observations were also made for the numerical results inside the text.     

Selective review of boundary element modelling for the interaction of deformable structures with water waves

A review was conducted of the use of the boundary element method as a solution technique for the nonlinear interaction of deformable structures and finite amplitude waves. The review concentrated on those areas in which modelling difficulties are anticipated: boundaries, waves, time domain analysis, fluid-structure interaction and a coupled finite element and boundary element model. Very little information was uncovered on the nonlinear fluid-structure interaction, although it is anticipated that the fluid domain would be modelled with a boundary element model and the structure would be modelled with a finite element model. The boundary element method appears to be a viable solution technique for the nonlinear interaction of deformable structures and finite amplitude waves.     

一致粘弹性人工边界及粘弹性边界单元

提出了一致粘弹性人工边界及粘弹性人工边界单元的概念,推导了二维一致粘弹性人工边界单元刚度及阻尼矩阵,并在其基础上使用矩阵等效原理实现了采用普通有限单元模拟的二维粘弹性边界单元。均匀半空间算例与成层半空间算例验证了粘弹性边界单元具有与集中粘弹性人工边界相同的精度,并且实施更为简便。     

Improved numerical method for time domain dynamic structure-foundation interaction analysis based on scaled boundary finite element method

Based on the reduced set of base function in scaled boundary finite element method (SBFEM), an improved time domain numerical approach for the dynamic structure-foundation interaction analysis was proposed. With reasonable choice of the number of base functions, the degrees of freedom on the structure-foundation interface were reduced and the associated computation for the calculation of convolution integral was greatly reduced. The results of this proposed approach applied to the calculation of a gravity dam and an arch dam. The acceleration frequency response functions were calculated and the influences affected by different reduced set of base functions as well as full set were compared. It was found that a higher degree of reduced set of base functions resulted in a significant increase of computational efficiency but a little bit of loss in accuracy. When the reduced set was decreased by 60%, the efficiency may be increased to up to five times, while the loss of accuracy of peak value of response will be less than 4%. It may be concluded that the proposed approach is suitable for large-scale structure-foundation interaction analysis.     

人工边界及地震动输入在有限元软件中的实现

粘弹性人工边界不仅在时间上是局部的,而且在空间上也是局部的,这种边界物理意义清晰、简单有效,且易于在有限元法中得以实现,与之相对于的地震动输入则是通过在边界上施加等效节点力实现的,等效节点力的大小与入射地震波波速成正比.本文利用通用有限元软件提供的弹簧阻尼单元模拟粘弹性边界,介绍了土-地下结构开放系统人工边界及地震动输...     

加权残数和有限元耦合法解弹性力学问题

提出了加权残数和有限元耦合法的思想,推导了求解弹性力学和薄板变曲问题的加权残数和有限元耦合法的公式,给出了算例,与理论解进行了比较,并阐述了本文方法的优点.     

解析层元法求解层状地基非轴对称荷载问题

从弹性层状地基非轴对称问题的解析解出发,推导出Hankel积分变换域内单层地基的解析层元,即对称的精确刚度矩阵;然后根据有限层法原理组合相邻层元得到总刚度矩阵,并结合边界条件,求解总刚度矩阵形成的代数方程,得到层状地基非轴对称问题在Hankel积分变换域内的解答;最后应用Hankel逆变换技术,得到物理域内的解。编制了相应的计算程序,分析了非轴对称荷载作用下多层地基沿径向的地表水平位移性状。     

Natural shape functions of a compressed Vlasov element

To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly.     

A general finite strip for the static and dynamic analyses of folded plates

In the conventional semi-analytical finite strip analysis of folded plates, the boundary conditions and the intermediate support conditions must be satisfied a priori. The admissible functions used as the longitudinal part of the displacement functions are sometimes difficult to find, and they are valid for specific conditions only. In this paper, a general finite strip is developed for the static and vibration analyses of folded plate structures. The geometric constraints of the folded plates, such as the conditions at the end and intermediate supports, are modelled by very stiff translational and rotational springs as appropriate. The complete Fourier series including the constant term are chosen as the longitudinal approximating functions for each of the displacements. As these displacement functions are more general in nature and independent of one another, they are capable of giving more accurate solutions. The potential problem of ill-conditioned matrices is investigated and the appropriate choice of the very stiff springs is also suggested. The formulation is done in such a way to obtain a unified approach, taking full advantage of the power of modern computers. A few numerical examples are presented for comparison with numerical results from published solutions or solutions obtained from the finite element method. The results show that this kind of strips is versatile, efficient and accurate for the static and vibration analyses of folded plates.