Optimum stacking sequence of composite laminates for maximum strength

A method is presented for maximum strength optimum design of symmetric composite laminates subjected to in-plane and transverse loadings. The finite element method based on shear deformation theory is used for the analysis of composite laminates. Ply orientation angles are chosen as design variables. The quadratic failure criterion which is meant to predict fracture, is used as an object function for optimum stacking sequence design of a laminated plate. The Broydon-Fletcher-Goldfarb-Shanno optimization technique is employed to solve the optimization problem effectively. Numerical results are given for various loading conditions, boundary conditions, and aspect ratios. The results show that the quadratic failure criterion such as Tsai-Hill theory is effective for the optimum structural design of composite laminates.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 393–404, May–June, 1995.     

环形板最大挠度极小化的优化设计*

本文讨论环形板的最大挠度极小化的优化设计.环形板承受任意的轴对称荷载.利用阶梯折算法,问题可以化为一个具有等式约束的标准的非线性规划问题.算例表明,本文的方法具有很多的优点.     

Evolution of the Stress–Strain State of a Three-Dimensional Plate Weakened by a Central Crack under Impulsive Tension

A method is developed to describe the formation of the stress–strain state in the vicinity of the tip of a stationary crack in a three-dimensional plate under dynamic loading. The energy model used to describe the formation of the stress concentration zone around the crack tip is modified to take into account the transient character of the loading process and the influence of the free surfaces of the plate on the stress–strain state of the central part of the sample. The method is useful for describing static and dynamic brittle fracture from a unified point of view.     

Towards the computation of minimum drag profiles in viscous laminar flow

A numerical method is given for the solution of certain optimum design problems of fluid mechanics. The profile of given area and smallest drag in a uniform laminar flow is computed. This profile is long and slim, its front end is shaped like a wedge of angle 90° and its rear end is shaped like a cusp. Owing to the numerical complexity of the problem the precision of the results is average (around 5%). However, this work is a good illustration of the theoretical method exposed previously and it shows how good precision can be obtained if one is prepared to pay for it. A numerical solution of the adjoint system of the stationary Navier-Stokes equation is also given; this equation will play an important role in optimum design in fluid mechanics.     

Design optimization and forming methods for toroidal composite shells

Based on the example of a toroidal membrane, a model for calculating the winding trajectory and the shape of a shell billet and its transformation into given surface elements, as well as for calculating the shape of the membrane under an internal pressure loading, is developed. The problem of choosing optimum design variables and manufacturing parameters of the membrane is also investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 147–164, March–April, 2006.     

Optimum design of laminated composite plates under dynamic excitation

An integrated model for optimum weight design of symmetrically laminated composite plates subjected to dynamic excitation is presented in this work. Optimum design procedure based on flexibility and strength criteria is presented. The objective is to determine the optimum thicknesses of the laminate layers and its optimum orientations without exhibiting any failure according to Tsai-Wu failure criterion. The finite element method, based on Mindlin plate theory, is used in conjunction with an optimization method in order to determine the optimum design. Newmark algorithm, as an implicit time integration scheme, is used to discretize the time domain and calculate the transient response of the laminated composite plate. Exterior penalty method is exploited for the constrained minimization procedure. Fletcher-Powell algorithm is used for the unconstrained minimization process. To verify the capability and efficiency of the proposed model, three examples are solved. The examples deal with flexibility and stress constraints for different boundary conditions under various dynamic excitations.     

Inexact de Novo programming for water resources systems planning

This study presents an interval de Novo programming (IDNP) approach for the design of optimal water-resources-management systems under uncertainty. The model is derived by incorporating the existing interval programming and de Novo programming, allowing uncertainties represented as intervals within the optimization framework. The developed IDNP approach has the advantages in constructing optimal system design via an ideal system by introducing the flexibility toward the available resources in the system constraints. A simple numerical example is introduced to illustrate the IDNP approach. The IDNP is then applied to design an inexact optimal system with budget limit instead of finding the optimum in a given system with fixed resources in a water resources planning case. The results demonstrate that the developed method efficiently produces stable solutions under different objectives. Optimal supplies of good-quality water are obtained in considering different revenue targets of municipal–industrial–agricultural competition under a given budget.     

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It is difficult to get an accurate optimum design when the experimental design area is very irregular under complex constraints. This paper constructs a random search algorithm for mixture experiments designed (MDRS). Firstly, generating an initial points set in areas with complex constraints by the Monte-Carlo method, then use MDRS algorithm iterative to approximate optimum set. By way of example verification, this method is effective. It can be used as a standard measure of other designs, that is the only effective when given superior to other designs approximate optimal solution.     

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.     

Dynamic Tension of a Plate Containing a Stationary Central Crack

A physically substantiated energy model of the formation of a stress concentration zone in the vicinity of the tip of a stationary crack under dynamic loading is developed by a combined theoretical and experimental approach. The hypothetical feasibility of describing the effects of an arbitrarily shaped load pulse on a stationary crack is demonstrated. Analytical expressions are derived for the dynamic stress intensity factor. A new mechanical interpretation of the stress intensity factor is proposed.     

板梁组合结构可靠性分析的随机边界元法

本文用随机边界元法分析了随机荷载作用下具有随机边界条件的正交各向异性板、梁组合结构的可靠性.文中首先给出正交各向异性板、梁组合结构的边界积分方程,进而基于随机边界元法建立了随机结构可靠性分析方法和得到用于计算正交各向异性板、梁组合结构可靠性指标的公式.算例表明了本文方法的有效性.     

带裂纹层合板能量释放率分析

为了进一步了解裂纹尖端应力场的特性,本文对复合材料层合板的界面裂纹作了分析.文中强调了能量释放率分量存在的条件,并给出能量释放率分量和应力强度因子间的关系式.结合经典板理论的分析结果,根据外荷作用及某些几何参数和材料多数,导出了一般复合材料层合板的应力强度因子的封闭形式解.为了得到在一般荷载条件下能量释放率的分量,必须分别确定模型混合参数Ω,文中讨论了确定参数Ω的方法,最后,应用本文方法于几种不同种类的复合材料层合板,证明其结果可应用于工程实践.     

基于平稳序列的沪深300股指期货最优套利点研究

基于正态分布和t分布的平稳序列前提,给出了沪深300股指期货跨期套利的最优套利点确定方法.通过对沪深300股指期货不同合约之间的差价进行平稳性检验,发现大部分差价具有平稳性,所以基本适用于给出的最优套利点分析方法.经过对5个平稳差价序列的最优套利点分析,发现△P_(12-07)=IF_(1212)-IF_(1207)和△P_(12-09)=IF_(1212)-IF_(1209)的套利期望收益较大,应该成为沪深300股指期货跨期套利的主要关注对象.     

Regularization of optimal design problems for bars and plates,part 1

In this paper, we consider a number of optimal design problems for elastic bars and plates. The material characteristics of rigidity of an elastic nonhomogeneous medium are taken as the control variables. A linear functional of the solutions to the equilibrium boundary-value problem is minimized under additional restrictions upon the control variables.Special variations of the control within a narrow strip provide a necessary condition for a strong local minimum (Weierstrass test). This necessary condition can be used for the detailed analysis of the following problems: bar of extremal torsional rigidity; optimal distribution of isotropic material with variable shear modulus within a plate; and optimal orientation of principal axes of elasticity in an orthotropic plate. For all of these cases, the stationary solutions violate the Weierstrass test and therefore are not optimal. This is because, in the course of the approximation of the optimal solution, the curve dividing zones occupied by materials with different rigidities displays rapid oscillations sweeping over a two-dimensional region. Within this region, the material behaves as a composite medium assembled of materials of the initial class.     

The thermoelastic problem for a halfspace with a semiinfinite elastic thermal insulator

Numerical conditions are given in an infinite and semiinfinite plate (heat insulator), which is connected by a vertical two-sided connection only with an elastic halfspace, in the interior of which is a concentrated source of heat, which generates a stationary heat field. The problem is reduced to the solution of an integral-differential equation of the Wiener-Hopf type with respect to the Fourier transform of the contact stress. Its exact solution is constructed using the factorization method, and the final solution is represented by a series with respect to Chebyshev-Laguerre polynomials. Calculations of bending moments and transverse forces are given in an infinite plate, semiinfinite, and infinite beam-rolling plates.Translated from Dinamicheskie Sistemy, No. 7, pp. 114–123, 1988.     

Spatial Regression Models,Response Surfaces,and Process Optimization

Abstract

Spatial regression models are developed as a complementary alternative to second-order polynomial response surfaces in the context of process optimization. These models provide estimates of design variable effects and smooth, data-faithful approximations to the unknown response function over the design space. The predicted response surfaces are driven by the covariance structures of the models. Several structures, isotropic and anisotropic, are considered and connections with thin plate splines are reviewed. Estimation of covariance parameters is achieved via maximum likelihood and residual maximum likelihood. A feature of the spatial regression approach is the visually appealing graphical summaries that are produced. These allow rapid and intuitive identification of process windows on the design space for which the response achieves target performance. Relevant design issues are briefly discussed and spatial designs, such as the packing designs available in Gosset, are suggested as a suitable design complement. The spatial regression models also perform well with no global design, for example with data obtained from series of designs on the same space of design variables. The approach is illustrated with an example involving the optimization of components in a DNA amplification assay. A Monte Carlo comparison of the spatial models with both thin plate splines and second-order polynomial response surfaces for a scenario motivated by the example is also given. This shows superior performance of the spatial models to the second-order polynomials with respect to both prediction over the complete design space and for cross-validation prediction error in the region of the optimum. An anisotropic spatial regression model performs best for a high noise case and both this model and the thin plate spline for a low noise case. Spatial regression is recommended for construction of response surfaces in all process optimization applications.     

Nonparametric quantile regression with heavy-tailed and strongly dependent errors

We consider nonparametric estimation of the conditional qth quantile for stationary time series. We deal with stationary time series with strong time dependence and heavy tails under the setting of random design. We estimate the conditional qth quantile by local linear regression and investigate the asymptotic properties. It is shown that the asymptotic properties are affected by both the time dependence and the tail index of the errors. The results of a small simulation study are also given.     

Minimum weight design of elastic cables

This paper is concerned with the minimum weight design of an elastic cable of variable cross section with both ends positioned at the same level. The cable is under the action of a uniformly distributed load. With the deflection of the cable given and the stress in the cable restricted, our objective is to determine the optimum distribution of the cross section. Calculus of variations with equality and inequality constraints is employed to find the necessary conditions of optimality. Efficiency of the optimum design evaluated from the comparison of an optimum cable with an equivalent cable of uniform cross section is studied. The best sag-span ratio of the optimum cable is also determined.     

Fluid–structure interaction solver for compressible flows with applications to blast loading on thin elastic structures

In this study, we report the development and application of a fluid–structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes a partitioned approach to strongly couple a sharp interface immersed boundary method-based flow solver with an open-source finite-element structure dynamics solver. The flow solver is based on a higher-order finite-difference method using a Cartesian grid, where it employs the ghost-cell methodology to impose boundary conditions on the immersed boundary. Higher-order accuracy near the immersed boundary is achieved by combining the ghost-cell approach with a weighted least squares error method based on a higher-order approximate polynomial. We present validations for two-dimensional canonical acoustic wave scattering on a rigid cylinder at a low Mach number and for flow past a circular cylinder at a moderate Mach number. The second order spatial accuracy of the flow solver was established in a grid refinement study. The structural solver was validated according to a canonical elastostatics problem. The FSI solver was validated based on comparisons with published measurements and simulations of the large-scale deformation of a thin elastic steel panel subjected to blast loading in a shock tube. The solver correctly predicted the oscillating behavior of the tip of the panel with reasonable fidelity and the computed shock wave propagation was qualitatively consistent with the published results. In order to demonstrate the fidelity of the solver and to investigate the coupled physics of the shock–structure interaction for a thin elastic plate, we employed the solver to simulate a 6.4 kg TNT blast loading on the thin elastic plate. The initial conditions for the blast were taken from previously reported field tests. Using numerical schlieren, the shock front propagation, Mach reflection, and vortex shedding at the tip of the plate were visualized during the impact of the shock wave on the plate. We discuss the coupling between the nonlinear dynamics of the plate and blast loading. The plate oscillates under the influence of blast loading and the restoration of elastic forces. The time-varying displacement of the tip of the plate is the superimposition of two dominant frequencies, which correspond to the first and second modes of the natural frequency of a vibrating plate. The effects of the material properties and length of the plate on the flow-induced deformation are briefly discussed. The proposed FSI solver is a versatile computational tool for simulating the impact of a blast wave on thin elastic structures and the results presented in this study may facilitate the design of thin structures subjected to realistic blast loadings.     

Stability of nonlinear viscoelastic systems under stochastic excitation

The dynamic behaviour of viscoelastic system with due account of finite deflections but under condition of small strains is described by the system of nonlinear integro-differential equations. On an example of a thin plate subjected to loads, which are assumed as random wide-band stationary noises and applied in the plate plane, the stability of nonlinear systems is considered. The stability in a case of finite deflections of the plate is considered as stability with respect to statistical moments of perturbations and almost sure stability. For the solution of the problem, a numerical method is offered, which is based on the statistical simulation of input stochastic stationary processes, which are assumed in the form of Gaussian ”colored” noises, and on the numerical solution of integro-differential or differential equations. The conclusion about the stability of the considered system is made on the basis of Lyapunov exponents. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)