Generalisations of Heyman's and Foulkes' theorems using dual formulation

Existing duality principles in structural optimisation are briefly reviewed and then they are extended to structures with segment-wise constant cross-sections. All theories are discussed in the particular context of optimal plastic beam design with symmetric convex specific cost functions and are confirmed by independent calculations on illustrative examples. It is shown that the optimal solution is always associated with a displacement field in which the mean absolute curvature value for each segment equals the subgradient of the specific cost function, with respect to the maximum absolute moment value for that segment. Moreover, the dual problem consists of the maximisation of the difference of two terms: the first one is the integral of the product of load and deflection (external work), and the second is the sum of products of segment lengths and the mean complementary cost values (taken with respect to the mean absolute curvature for that segment). Finally, some tentative proposals for a class of non-convex optimisation problems are presented. For special cases, the proposed general statements reduce to theorems by Heyman, Foulkes and Hemp.     

Resonant neutron filters in elemental analysis and radiography

Translated from Atomnaya Énergiya, Vol. 67, No. 4, pp. 271–274, October, 1989.     

Multifunctional alkylphenol additive

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 14–15, February, 1989.     

Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

Mechanisms of Active Fuzzy Expertise

Consideration was given to the decision making procedures based on the fuzzy messages of experts whose preferences on the set of collective decisions can also be fuzzy.     

Power system analysis using space-vector transformation

In this paper, the space-vector transformation used in machine vector control is applied to power system analysis. The proposed method is used to model electric machines, power electronic converters, transformers, and transmission lines and to analyze power sources and loads with different connections (delta and wye). This method can also be applied to analyze steady-state (or transient phenomena) and unbalanced sources, including harmonics. Models obtained with this method are as simple as those of the per-phase approach. With the space-vector transformation, instantaneous active and reactive power concepts can be generalized, and new power system control strategies can be developed when power electronic converters are used. Steady-state, transient behavior, and harmonic analyses examples and applications are presented to illustrate the performance and advantages of the proposed method. This method can be extended to unbalanced systems (e.g., unsymmetric faults) using instantaneous symmetrical components in polyphase balanced circuits.     

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components ε* _xx and ε* _yy . For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t=ε* _yy /ε* _xx . We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t=1) and those with pure shear misfit (t=−1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (−1<t<1; t ≠ 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0<t<1. For systems which allow an invariant line (−1≤t<0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0<t≤1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.