共查询到20条相似文献,搜索用时 46 毫秒
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在最优控制理论中根据模拟理论思想发展了塑性力学和接触力学中的参变量变分原理, 并建立了控制输入受限的线性二次(linear quadratic, LQ)最优控制问题的求解新方程---耦合的Hamilton正则方程与线性互补方程. 通过将连续时间离散成一系列等间距时间区段, 在离散时域内采用参数二次规划方法给出数值求解输入受限的LQ最优控制问题的新算法. 数值仿真验证了该算法在求解控制输入受限的LQ最优控制问题中的有效性, 并且该算法具有较快的收敛性, 在大步长下具有较高的计算精度. 相似文献
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弹性力学Hamilton方法广义解的适定性 总被引:1,自引:0,他引:1
首先引入了Hamilton体系中平面应力弹性力学问题正则方程的Galerkin变分方程,证明了Galerkin变分方程和目前文献中所用的Ritz变分方程的等价性,以及相应广义解的适定性,从而为目前的数值方法提供了理论基础。从证明过程中可以看到广义解实际上是Ritz变分泛函的一个鞍点。 相似文献
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A new smooth gap function for the box constrained variational inequality problem(VIP) is proposed based on an integral global optimality condition.The smooth gap function is simple and has some good differentiable properties.The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function.The conditions,under which any stationary point of the optimization problem is the solution to the box constrained VIP,are discussed.A simple frictional contact problem is analyzed to show the applications of the smooth gap function.Finally,the numerical experiments confirm the good theoretical properties of the method. 相似文献
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《力学快报》2022,12(5):100368
The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus. Not only can the combination of and derivatives be beneficial to obtaining higher convergence order in numerical analysis, but also it prompts the time-scale numerical computational scheme to have good properties, for instance, structure-preserving. In this letter, a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed. By using the time-scale discrete variational method and calculus theory, and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems, the corresponding discrete Hamiltonian principle can be obtained. Furthermore, the time-scale discrete Hamilton difference equations, Noether theorem, and the symplectic scheme of discrete Hamiltonian systems are obtained. Finally, taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples, they show that the time-scale discrete variational method is a structure-preserving algorithm. The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed. 相似文献
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A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints. 相似文献
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为了保证直升机在舰船上的安全性,必须使用系留设备将直升机系留在舰船上。直升机的系留问题可简化为由机身刚体、索具和起落架组成的杆件系统,索具只承受拉力而不承受压力,起落架只承受压力而不承受拉力。因此,直升机系留问题为典型的强非线性问题,需要发展有效的求解算法。在考虑大变形的情况下,基于参变量变分原理建立了求解直升机系留载荷的高性能计算方法。 该方法利用参变量变分原理能够准确判断索具和起落架的拉压状态,并将材料非线性静力问题转换为线性静力互补问题求解,极大地提高了结果的收敛性。数值算例中,通过与有限元通用软件NASTRAN和ABAQUS计算结果比较,证实了该方法的精确性、收敛性及高效性。 相似文献
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Based on the fluid-structure coupling theory, a localized variational principle for analyzing the sound radiation from elastic
structure submerged in water due to harmonic excitations is presented. It will be a powerful tool to formulate various numerical
methods for steady response of structural-acoustic systems. By means of this variational principle a hybrid element method,
in which an analytical solution valid in most of the surrounding water is incorporated with finite elements distributed in
the structure and its neighboring water, is devised. Computational examples are then given to demonstrate its high accuracy
and time saving.
The project supported by the National Natural Science Foundation of China (10172038) and the Doctoral Program Foundation of
Institution of Higher Education of China (20040487013). The English text was polished by Yunming Chen. 相似文献
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D. Auroux 《国际流体数值方法杂志》2009,61(8):911-929
We study in this paper a new data assimilation algorithm, called the back and forth nudging (BFN). This scheme has been very recently introduced for simplicity reasons, as it does not require any linearization, or adjoint equation, or minimization process in comparison with variational schemes, but nevertheless it provides a new estimation of the initial condition at each iteration. We study its convergence properties as well as efficiency on a 2D shallow water model. All along the numerical experiments, comparisons with the standard variational algorithm (called 4D‐VAR) are performed. Finally, a hybrid method is introduced, by considering a few iterations of the BFN algorithm as a preprocessing tool for the 4D‐VAR algorithm. We show that the BFN algorithm is extremely powerful in the very first iterations and also that the hybrid method can both improve notably the quality of the identified initial condition by the 4D‐VAR scheme and reduce the number of iterations needed to achieve convergence. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 相似文献
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This paper presents the optimization of unsteady Navier–Stokes flows using the variational level set method. The solid–liquid interface is expressed by the level set function implicitly, and the fluid velocity is constrained to be zero in the solid domain. An optimization problem, which is constrained by the Navier–Stokes equations and a fluid volume constraint, is analyzed by the Lagrangian multiplier based adjoint approach. The corresponding continuous adjoint equations and the shape sensitivity are derived. The level set function is evolved by solving the Hamilton–Jacobian equation with the upwind finite difference method. The optimization method can be used to design channels for flows with or without body forces. The numerical examples demonstrate the feasibility and robustness of this optimization method for unsteady Navier–Stokes flows.Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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首先改进文[1]的互补变分原理。再建议一种较为普遍性的方法,导出精确的边界积分方程。最后给出变分有限元及边界元解,算例证实有限元格式及迭代方式有效。 相似文献
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基于Hamilton体系的辛半解析法在各向异性电磁波导中的应用 总被引:1,自引:0,他引:1
力学中的Hamilton体系使用对偶变量来描述问题,而电磁场正好有电场和磁场这一对对偶变量。本文将力学中的Hamilton体系应用到电磁波导问题。根据电磁波导的Hamilton体系理论,辛几何可用于任意各向异性材料。将横向的电场和磁场构成对偶向量,基于Hamilton变分原理做半解析横向离散,并保持结构辛体系。本文以各向异性材料电磁波导为例,求解了问题的辛本征值,得到了镜像线的色散曲线。 相似文献
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A finite‐volume multi‐stage (FMUSTA) scheme is proposed for simulating the free‐surface shallow‐water flows with the hydraulic shocks. On the basis of the multi‐stage (MUSTA) method, the original Riemann problem is transformed to an independent MUSTA mesh. The local Lax–Friedrichs scheme is then adopted for solving the solution of the Riemann problem at the cell interface on the MUSTA mesh. The resulting first‐order monotonic FMUSTA scheme, which does not require the use of the eigenstructure and the special treatment of entropy fixes, has the generality as well as simplicity. In order to achieve the high‐resolution property, the monotonic upstream schemes for conservation laws (MUSCL) method are used. For modeling shallow‐water flows with source terms, the surface gradient method (SGM) is adopted. The proposed schemes are verified using the simulations of six shallow‐water problems, including the 1D idealized dam breaking, the steady transcritical flow over a hump, the 2D oblique hydraulic jump, the circular dam breaking and two dam‐break experiments. The simulated results by the proposed schemes are in satisfactory agreement with the exact solutions and experimental data. It is demonstrated that the proposed FMUSTA schemes have superior overall numerical accuracy among the schemes tested such as the commonly adopted Roe and HLL schemes. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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This paper develops a new approach to construct variational integrators. A simplified unconventional Hamilton’s variational principle corresponding to initial value problems is proposed, which is convenient for applications. The displacement and momentum are approximated with the same Lagrange interpolation. After the numerical integration and variational operation, the original problems are expressed as algebraic equations with the displacement and momentum at the interpolation points as unknown variables. Some particular variational integrators are derived. An optimal scheme of choosing initial values for the Newton-Raphson method is presented for the nonlinear dynamic system. In addition, specific examples show that the proposed integrators are symplectic when the interpolation point coincides with the numerical integration point, and both are Gaussian quadrature points. Meanwhile, compared with the same order symplectic Runge-Kutta methods, although the accuracy of the two methods is almost the same, the proposed integrators are much simpler and less computationally expensive. 相似文献
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Christian Miehe Björn Kiefer Daniele Rosato 《International Journal of Solids and Structures》2011,48(13):1846-1866
This paper outlines a new variational-based modeling and computational implementation of macroscopic continuum magneto-mechanics involving non-linear, inelastic material behavior, with a special focus on dissipative magnetostriction. It is based on a constitutive variational principle that optimizes a generalized incremental work function with respect to the internal state variables. In an incremental setting at finite time steps, this variational problem defines a quasi-hyper-magnetoelastic potential for the stresses and the magnetic induction, and incorporates energy storage as well as dissipative mechanisms. The existence of this potential further allows the incremental boundary-value problem of quasi-static inelastic magneto-mechanics to be recast into a principle of stationary incremental energy. The second focus of this paper is on the careful construction of the energy storage and dissipation functions for the model problem of hysteretic magnetostriction at the macroscopic level. It is then demonstrated that the proposed model is capable of predicting the ferromagnetic and field-induced strain hysteresis curves characteristic of magnetostrictive material response in good agreement with experiments. The numerical solution of the coupled non-linear boundary-value problem is based on a monolithic multi-field finite element implementation. As a consequence of the proposed incremental variational principle, the discretization of the multi-field problem appears in a compact symmetric format. In this sense, the proposed formulation provides a canonical framework for the simulation of boundary-value-problems in dissipative magnetostriction at the macro-level. The performance of the proposed algorithm is tested by application to relevant numerical examples. 相似文献