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基于Engel提出的构造复Logistic映射z←λz(1-z)的Julia集内部结构的算法,作者构造了一系列复映射Z←Z^α+c(α∈R)的广义Mandelbrot.Julia集(简称广义M-J集)的内部结构图。采用复变函数理论和计算机制图相结合的实验数学方法,作者研究了的广义M-J集内部的结构拓扑不变性和裂变演化规律。研究表明广义M-J集的内部具有分形特征,小数阶广义M-J集的内部出现了错动和断裂,且其断裂和演化依赖于主幅角范围的选取。 相似文献
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陈杰华 《四川联合大学学报》1998,2(5):20-23,44
利用牛顿迭代法求解复系数多项式的根,是一种特殊的复有理映射,本文探讨多项式z^4+(λ-1)z-λ的牛顿变换特性,其中λ是复变量,并图示了三种λ参数情况下的临界点的轨道性能。 相似文献
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利用n维参数L系统描述了超复数空间广义Mandelbrot集和Julia集,给出了描述算法和实验所得图形,并对四元数广义M-J集的动力学特征进行了理论上的分析和探讨.经过实验发现,四元数广义M-J集在保留了复平面M-J集特征的基础上,还有一些特殊的性质,如广义M集在三维虚轴截面上的拓扑结构等同于球体,四元数Julia集在参数c同模同实部的情况下保持着结构的一致性.实验结果表明,n维参数L系统字母表较为简洁,包含信息量大,可以有效的描述诸如广义M-J集和四元数广义M-J集的分形集. 相似文献
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利用修正的牛顿-谐波平衡法建立了非线性奇异振子的解析逼近周期和周期解.通过改写控制方程和选取简单、合适的校正项对牛顿-谐波平衡法进行了修正.构造的两个解析逼近周期和周期解不仅在振幅和参数全部取值范围内有效且能快速地收敛到精确解;两个逼近周期与精确周期的百分比误差分别低于0.92%和0.09%,后者比已有结果精度高。 相似文献
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采用简单的牛顿迭代法迭代,并将非线性方程视为非线性的动力学系统,利用使系统产生混沌的Julia集
的点求解方程的全部实数解,而Julia集的点在Jocobi矩阵行列式的值为零的解集的邻域内,给定矩阵的行列式的
值的表达式的一些变量为已知,仅有一个变量未知,把它转化为一元非线性方程,进而求出一元非线性方程全部
解. 再在给定变量的邻域内取定给定变量,根据一元非线性方程的全部解以确定该变量的搜索范围,运用粗、精迭
代法求解全部位置解.运用该算法编写了MATLAB程序,对一般机器人6-SPS机构的全部位置正解问题进行了
研究,得出了Jocobi矩阵的通用表达式,从而得到了其全部位置正解,为实际的6-SPS机构的位置正解问题提供了
全新的方法. 相似文献
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文章提出了运用拉绳位移传感器构建测量场,并采用牛顿迭代法求解飞机大部件对接过程中的位置和姿态的方法。通过对拉绳位移传感器的固定布局和建立约束条件,根据拉绳传感器测出的6组点间的距离,建立位姿求解的理论模型,并运用牛顿迭代法对大部件位姿进行求解,求解结果与理论位姿对比显示,位置偏移最大误差在0.07 mm,姿态角旋转最大误差在0.0004°,可以用于飞机大部件对接位姿解算。该方法求解位姿时不使用额外的非接触式测量仪器,避免了建立复杂的光学测量场和复杂的空间位姿解算。 相似文献
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复多值函数动力系统的广义M-J分形图 总被引:1,自引:0,他引:1
在研究一般复幂函数f(z)=z^α iβ C的动力系统分形图的结构时,针对在其构造其动力系统分形图时,无法确定其符合Mandelbrot集定义的迭代初始点Z。而无法得到严格意义下的Mandelbrot集分形图的问题,提出一种研究动力系统性质的方法,即构造由这些多值函数各分枝组成的随机复迭代动力系统的广义Mandelbrot集与广义Julia集。 相似文献
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A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures
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Ke Liang Mostafa M. Abdalla Qin Sun 《International journal for numerical methods in engineering》2018,113(10):1541-1560
The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems. 相似文献
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P. PAPADOPOULOS R. L. TAYLOR 《International journal for numerical methods in engineering》1996,39(15):2635-2646
A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes. 相似文献
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运用一维混沌映射产生初始点,再映射到变量区间,为牛顿迭代初值进行求解非线性方程组,提出了基于混沌映射的牛顿迭代法求解非线性方程组的新方法。对曲柄滑块机构进行了研究,给出了算例。该方法简单、实用,为实际机构的设计提供了多种选择方案,为机构学设计提供了新方法。 相似文献
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The basis is given of the possibility of constructing an asymptotically stable self-contained inertial navigation system. 相似文献
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G. Alfano F. Marmo L. Rosati 《International journal for numerical methods in engineering》2007,72(8):924-963
We present a numerical procedure, based upon a tangent approach, for evaluating the ultimate limit state (ULS) of reinforced concrete (RC) sections subject to axial force and biaxial bending. The RC sections are assumed to be of arbitrary polygonal shape and degree of connection; furthermore, it is possible to keep fixed a given amount of the total load and to find the ULS associated only with the remaining part which can be increased by means of a load multiplier. The solution procedure adopts two nested iterative schemes which, in turn, update the current value of the tentative ultimate load and the associated strain parameters. In this second scheme an effective integration procedure is used for evaluating in closed form, as explicit functions of the position vectors of the vertices of the section, the domain integrals appearing in the definition of the tangent matrix and of the stress resultants. Under mild hypotheses, which are practically satisfied for all cases of engineering interest, the existence and uniqueness of the ULS load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved. An extensive set of numerical tests, carried out for rectangular, L‐shaped and multicell sections shows the effectiveness of the proposed solution procedure. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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符号函数是求解来自控制论中相关的Lyapunov方程和Riccati方程的有力工具,它也用来解某些特征值问题和计算不变子空间.本文给出了求矩阵符号函数的割线法,证明了该方法对于特殊的初始矩阵是全局超线性收敛的,并给出了数值试验,并将割线法与Newton法进行了比较,理论上和数值上均验证了割线法是求矩阵符号函数的有效数值方法. 相似文献
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Algorithmically imposed thermodynamic compliance for material models in mechanical simulations using the AIM method
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C. F. Dunant E. C. Bentz 《International journal for numerical methods in engineering》2015,104(10):963-982
Thermodynamic irreversibility can be imposed on empirical material behaviour by using an appropriate algorithm which takes the path‐dependence of the degradation process into account. This new algorithm, Algorithmically Imposed Mechanics (AIM), for algorithmically irreversible mechanics, is described, and the convergence and unicity of the solutions obtained are proven. AIM is applicable to a range of mechanical behaviour and is demonstrated to work in conjunction with non‐local damage with rotating cracks as well as a mixed plastic and damage behaviour. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献