Optimization of cyclindrical shells of fiber-reinforced composite materials

Problems of optimizing nonelastic circular shells are considered. The material of the shells is assumed to be a fiber-reinforced composite with fibers unidirectionally embedded in a relatively less stiff but ductile metallic matrix so that the material has the yield surface suggested by Lance and Robinson. The shell is subjected to an impulsive loading of short-time periods generating initial kinetic energy. During plastic deformation of the shell the initial kinetic energy is transformed into the plastic strain energy. The shell thickness is assumed to be piecewise constant. Various thicknesses and coordinates of the rings, where the thickness has jumps, are preliminarily unspecified. We look for a shell design for which the maximum residual deflection has a minimum value for the total weight given. The alternative problem of minimizing the shell weight for the maximum deflection given is also studied.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Octobe, 1995.Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 65–71, January–February, 1996.     

Analytical solution of coupled soil erosion and consolidation equations by asymptotic expansion approach

In this work, one-dimensional approximation of internal erosion taking place in a soil made from sand and clay mixture was considered. The clay phase that is susceptible to experience erosion under water flow discharge was assumed to be small. A new erosion law fixing the initiation threshold of erosion and integrating the effect of soil consolidation on internal erosion was proposed. Conversely, the effect of erosion on elastic soil deformation was also integrated through damage mechanics concepts. Asymptotic expansion of the coupled equations in terms of a perturbation parameter linked to the total amount of internal erosion that is likely to occur has been performed. This has enabled to view the internal erosion phenomenon occurring inside the soil as a perturbation affecting the classical soil consolidation equation, and further to evaluate the critical discharge gradient for which internal erosion starts. Equations at order zero that are provided by the asymptotic expansion were exactly integrated while an adequate finite difference scheme was introduced to solve the equations at order one. A parametric study was conducted after that in order to assess effects of the main factors on internal erosion and soil deformation.     

Energy considerations of the flow behind a plane hydromagnetic shock

Similarity solutions describing the flow behind a plane hydromagnetic shock propagating with a constant velocity into a uniform ideal gas at rest in the presence of a transverse magnetic field are obtained. The gas is assumed to be infinitely electrically conducting, inviscid and non-heat conducting. The gain in the total energy of the flow between the shock and the inner expanding surface is assumed to be time-dependent. The variations of the percentages of the magnetic, internal and kinetic energies with the strength of the shock are studied. It is shown that there exists two values of the strength of the shock at which equipartition of the internal and kinetic energies of the flow between the shock and the inner expanding surface can occur.     

Stability and optimal control of thermomechanical processes with non-convex free energies of Ginzburg–Landau type

In this paper we study a coupled non-linear system of partial differential equations that models the dynamics of structural phase transitions in a one-dimensional non-viscous and heat-conducting solid. The corresponding Helmholtz free energy density is assumed in Ginzburg–Landau form; to allow for phase transitions and hysteresis phenomena, it is not assumed convex in the order parameter. It is shown that the solution of the system depends continuously upon the data, and we prove an existence result for an associated optimal control problem.     

Phase change problems with temperature dependent constraints for the volume fraction velocities

A class of nonlinear systems of parabolic PDEs is considered as a mathematical model for phase change phenomena arising in binary mixtures. We use the volume fraction of one of the components as an order parameter in our systems. Therefore, our system consists of two kinetic equations for the internal energy and order parameter which are derived in the non-smooth thermomechanics theory. In this paper we give a general treatment for our system and establish an existence result by applying the Schauder's fixed point theory with the subdifferential operator techniques.     

Derivation of the method of characteristics for the fluid dynamic solution of flow advection along porous wall channels

This paper describes in detail a novel formulation of the method of characteristics for its application to solve one-dimensional compressible unsteady non-homentropic flow advected along porous wall channels. In particular, the method is implemented into a wall-flow monolith Diesel particulate filter model whose purpose is the pressure drop prediction. The flow inside the monolith channels is considered to be one-dimensional and the flow through the porous wall treated as a source term agree with the Darcy’s law. The flow dynamic behaviour at internal nodes of the channels is solved by means of shock capturing methods, whereas the end nodes, or boundary conditions, are solved applying the method of characteristics. The derived solution in this study of the Riemann variables and the entropy level includes the variation along the space–time plane due to cross-section area changes, friction and heat transfer as traditionally stated, but also takes into account the key influence on every line of the flow leaving or entering to the channels through the porous walls.     

A nonlinear fracture differential kinetic model to depict chaotic atom motions at a fatigue crack tip based on the differentiable manifold methodology

A nonlinear differential kinetic model describing dynamical behaviours of an atom at a fatigue crack tip is developed in this paper. It is assumed that the forces acted on this atom by its surrounding atoms consist of the following three components: (1) an elastic restoring force governed by Leonard-Jones potential, which describes the elastic interaction between atoms; (2) a nonlinear damping force proportional to its velocity through a linear function of its displacement as a coefficient that empirically simulates the energy loss from the crack tip to its surroundings; (3) an external remote driving force to represent thermally activated energy supplied to the crack tip from the surroundings. Based on these assumptions of the interaction forces between the atoms around the crack tip, a nonlinear dynamic equation describing the motion of the atom at a crack tip using the Newton’s second principle is derived. For a periodic external force and a random one influenced by parameters omitted, deterministic and a stochastic analyses on the dynamic equation obtained above are completed. Based on the theories of the Hopf bifurcation, global bifurcation and stochastic bifurcation, the extent and some possible implications of the existence of atomic-scale chaotic and stochastic bifurcative motions involving the fracture behaviour of actual materials are systematically and qualitatively discussed and the extreme sensitivity of chaotic motions to minute changes in initial conditions is explored. As demonstrated in the paper, chaotic behaviour may be observed in the case of a larger amplitude of the driving force and a smaller damping constant. The white noise introduced in the atomistic motion process may leads to a drift of the divergence point of the nonlinear stochastic differential kinetic system in contrast to the homoclinic divergence of the nonlinear deterministic differential kinetic system.     

功能梯度条硬币型裂纹扭转冲击响应

研究非均匀条中硬币型裂纹的扭转冲击问题．材料的剪切模量假定按特定的梯度变化．采用Laplace 和Hankel 变换将问题化为求解Fredholm积分方程,通过将Bessel函数渐进展开获得裂纹尖端动态应力场．考查非均匀参数和功能梯度条高度对裂尖动态断裂行为的影响．动应力强度因子和能量密度因子的清晰表达式表明,作为裂纹扩展力,对于这里所研究的问题,二者是等价的．动应力强度因子的数值结果显示,增加剪切模量的非均匀参数可以抑制动应力强度因子的幅度,而条形域的高度对动态断裂特性的影响较小．     

A computationally efficient method for modeling flexible robots based on the assumed modes method

In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method.The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language.The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples.     

Construction of kinetic models for metabolic reaction networks: Lessons learned in analysing short-term stimulus response data

Construction of dynamic models of large-scale metabolic networks is one of the central issues in the engineering of living cells. However, construction of such models is often hampered by a number of challenges, for example, data availability, compartmentalization and parameter identification coupled with design of in vivo perturbations. As a solution to the latter, short-term perturbation experiments are proposed and are proven to be a useful experimental method to obtain insights into the in vivo kinetic properties of the metabolic pathways.

The aim of this work is to construct a kinetic model using the available experimental data obtained by short-term perturbation experiments, where the steady state of a glucose-limited anaerobic chemostat culture of Saccharomyces cerevisiae was perturbed. In constructing the model, we first determined the steady-state flux distribution using the data before the glucose pulse and the known stoichiometry. For the rate expressions, we used approximative linlog kinetics, which allows the enzyme–metabolite kinetic interactions to be represented by an elasticity matrix. We performed a priori model reduction based on timescale analysis and parameter identifiability analysis allowing the information content of the experimental data to be assessed. The final values of the elasticities are estimated by fitting the model to the available short-term kinetic response data.

The final model consists of 16 metabolites and 14 reactions. With 25 parameters, the model adequately describes the short-term response of the cells to the glucose perturbation, pointing to the fact that the assumed kinetic interactions in the model are sufficient to account for the observed response.     

多个正态总体均值相等的VDR检验

本文将随机估计由一维参数扩展至多维参数,基于随机估计的密度函数提出VDR检验.在总体方差已知和未知的两种情形下,本文讨论多个正态总体均值是否相同的VDR检验过程,而且得到精确的检验.单因素方差分析是VDR检验的特例.模拟研究表明,VDR检验是一个普遍适用的方法.     

Mass,momentum and energy conservation laws in zero-pressure gas dynamics and δ-shocks: II

We study δ-shocks in a one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers (see References) this system is considered in the form of mass, momentum and energy conservation laws. In order to define such singular solutions, special integral identities are introduced which extend the concept of classical weak solutions. Using these integral identities, the Rankine–Hugoniot conditions for δ-shocks are obtained. It is proved that the mass, momentum and energy transport processes between the area outside the of one-dimensional δ-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving δ-shock wave front are going on. At the same time the total kinetic energy transforms into total internal energy.     

研究金属中激波构造与衰减的一个物理模型

本文给出了研究金属中激波构造与衰减的一个物理模型.为了建立高速形变下材料的本构方程和研究激波过渡带的构造,需要考虑二个独立的理论方面.首先,将比内能分解成弹性压缩能和弹性形变能,而将形变能作为弹性应变和熵的函数展开到三阶项,其中考虑了热与机械能的耦合效应.其次,从位错动力学角度建议了一个塑性松弛函数以便描述高温、高压下塑性流动的特性.另外,本文给出了一个常微分方程组用以计算定态激波过渡带中各状态变量的分布以及激波的厚度.倘若假定在激波上熵的跳跃可以忽略,并用Hugoniot压缩模量代替等熵压缩摸量,可以获得一个分析解.最后,本文还提出了求解平板对称碰撞中激波波头衰减的一个近似方法。     

Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H _∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H _∞ performance. The derived methods can be applied to the robust H _∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).     

Mixed-integer minimax dynamic optimization for structure identification of glycerol metabolic network

Cell metabolism is a dynamic regulation process, in which its network structure and/or regulatory mechanisms can change constantly over time due to internal and external perturbations. This paper models glycerol metabolism in continuous fermentation as a nonlinear mixed-integer dynamic system by defining the time-varying metabolic network structure as an integer-valued function. To identify the dynamic network structure and kinetic parameters, we establish a mixed-integer minimax dynamic optimization problem with concentration robustness as its objective functional. By direct multiple shooting strategy and a decomposition approach consisting of convexification, relaxation and rounding strategy, the optimization problem is transformed into a large-scale approximate multistage parameter optimization problem. It is then solved using a competitive particle swarm optimization algorithm. We also show that the relaxation problem yields the best lower bound for the optimization problem, and its solution can be arbitrarily approximated by the solution obtained from rounding strategy. Numerical results indicate that the proposed mixed-integer dynamic system can better describe cellular self-regulation and response to intermediate metabolite inhibitions in continuous fermentation of glycerol. These numerical results show that the proposed numerical methods are effective in solving the large-scale mixed-integer dynamic optimization problems.     

From bi-stability to chaotic oscillations in a macroeconomic model

In this paper a discrete-time economic model is considered where the savings are proportional to income and the investment demand depends on the difference between the current income and its exogenously assumed equilibrium level, through a nonlinear S-shaped increasing function. The model can be ultimately reduced to a two-dimensional discrete dynamical system in income and capital, whose time evolution is “driven” by a family of two-dimensional maps of triangular type. These particular two-dimensional maps have the peculiarity that one of their components (the one driving the income evolution in the model at study) appears to be uncoupled from the other, i.e., an independent one-dimensional map. The structure of such maps allows one to completely understand the forward dynamics, i.e., the asymptotic dynamic behavior, starting from the properties of the associated one-dimensional map (a bimodal one in our model). The equilibrium points of the map are determined, and the influence of the main parameters (such as the propensity to save and the firms' speed of adjustment to the excess demand) on the local stability of the equilibria is studied. More important, the paper analyzes how changes in the parameters' values modify both the asymptotic dynamics of the system and the structure of the basins of the different and often coexisting attractors in the phase-plane. Finally, a particular “global” (homoclinic) bifurcation is illustrated, occurring for sufficiently high values of the firms' adjustment parameter and causing the switching from a situation of bi-stability (coexistence of two stable equilibria, or attracting sets of different nature) to a regime characterized by wide chaotic oscillations of income and capital around their exogenously assumed equilibrium levels.     

Robust output feedback stabilization for two-dimensional continuous systems in roesser form

This paper considers the problem of robust stabilization via dynamic output feedbackcontrollers for uncertain two-dimensional continuous systems described by the Roesser's state space model. The parameter uncertainties are assumed to be norm-bounded appearing in all the matrices of the system model. A sufficient condition for the existence of dynamic output feedback controllers guaranteeing the asymptotic stability of the closed-loop system for all admissible uncertainties is proposed. A desired dynamic output feedback controller can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.     

Estimation of parameter matrices based on measured data

Finite element structural updating based on measured data may inherent significant errors due to uncertainties in the updated physical parameter matrices. This study presents analytical equations to estimate the change in the physical parameter matrices based on the measured modal data of dynamic systems and the measured displacement data of static systems. The equations for the parameter estimation are derived by minimizing cost functions in the satisfaction of the eigenvalue equation, the mode shape orthogonality requirements for the dynamic system, and the satisfaction of the measured displacement data for the static systems. The proposed method utilizes the Moore–Penrose inverse for the inverse of the rectangular matrices without using Lagrange multipliers. Comparing the analytical results with Berman & Nagy’s method and Yang & Chen’s method, this study demonstrates that the derived equations take simpler forms and produce more accurate results. The proposed method can be widely utilized in predicting static or dynamic parameter matrices for the design and analysis of any structure.     

Nonlocal coupled photo-thermoelasticity analysis in a semiconducting micro/nano beam resonator subjected to plasma shock loading: A Green-Naghdi-based analytical solution

In this article, coupled photo-thermoelasticity analysis is carried out using an analytical method in a semiconducting micro/nano beam resonator, considering Green – Naghdi theory (with energy dissipation) and small scale effects. The governing equations for temperature and displacement fields are derived using Eringen nonlocal theory combined with Rayleigh beam theory. One end of the assumed semiconducting MEMS/NEMS is excited by three types of suddenly increasing carrier density and temperature as the plasma and thermal shock loading. The transient behaviours of carrier density field are studied and the effects of disturbances in plasma field on other fields including temperature and deflection are obtained using the proposed analytical solution. The presented analytical solution is based on Laplace transform. To find the dynamic and transient behaviours of fields’ variables in time domain, an inversion Laplace technique is utilized, which is called Talbot method. The effects of small scale parameter and dimensions of the semiconducting micro/nano beam on the dynamic behaviours of fields’ variables are discussed in detail. The axial wave propagation and the distribution of fields’ variables along axial direction are studied at various times.     

Energy cycle of brushless DC motor chaotic system

The vector field of the brushless DC motor (BLDCM) chaotic system is regarded as the force field of a pure mechanical system via the transformation of Kolmogorov system. The BLDCM force field is decomposed into four types of torque: inertial, internal, dissipative, and generalized external torque. The forcing effect of each term in the force field is identified via the analogue of the electrical and mechanical system. The BLDCM energy transformation of four forms of energy—kinetic, potential, dissipative, and generalized external is investigated. The physical interpretation of force decomposition and energy exchange is given. The rate of change of the Casimir energy is equivalent to the power exchanged between the dissipative energy and the energy supplied to the motor, and it governs the different dynamic modes. A simple and optimal supremum bound for the chaotic attractor is proposed using the Casimir function and optimization.