On the search of a potential displacement surface with the use of the local variation method

The purpose of the article is to develop some basic conceptual provisions, algorithm and method of the search of the surface of the smallest resistance to shift, based on the minimization of durability functionality. The algorithm uses the approach, based on the direct iteration of various trial displacement surfaces and the selection of the surface with the minimum functionality value from these surfaces with the method of local variations. The coefficients allowing to estimate the possibility of rocks destruction at various sites of this surface are offered. The results of the search of a potential destruction surface for a pit board are given as an example.

Unstable Manifold of Hénon Map

A new algorithm is presented for computing one dimensional unstable manifold of a map and Hénon map is taken as an example to test the performance of the algorithm. The unstable manifold is grown with new point added at each step and the distance between consecutive points is adjusted according to the local curvature. It is proved that the gradient of the manifold at the new point can be predicted by the known points on the manifold and in this way the preimage of the new point could be located immediately. During the simulation, it is found that the unstable manifold of Hénon map coincides with its direct iteration when canonical parameters are chosen which means order is obtained out of chaos. In the other several groups of parameters the two branches of the unstable manifolds are nearly symmetric, and they serve as the borderline of the Hénon map iteration sequence. We hope that this would contribute to the further exploration of Hénon map.

ABS-type methods for solving full row rank linear systems using a new rank two update

ABS mthods are direct iteration methods for solving linear systems where the i-th iterate satisfies the first i equations, and therefore a system on m equations is solved in at most m ABS steps. In this paper, using a new rank two update of the Abaffian matrix, we introduce a class of ABS-type methods for solving full row rank linear equations, where the i-th iterate solves the first 2i equations. So, termination is achieved in at most ⌊(m + 1)/2⌋ steps. We also show how to decrease the dimension of the Abaffian matrix by choosing appropriate parameters.

Damage Identification in Continuum Structures From Vibration Modal Data

ABSTRACTA novel procedure for damage identification of continuum structures is proposed, where both the location and the extent of structural damage in continuum structures can be correctly determined using only a limited amount of measurements of incomplete modal data. On the basis of the exact relationship between the changes of structural parameters and modal parameters, a computational technique based on direct iteration and directly using incomplete modal data is developed to determine damage in structure. Structural damage is assumed to be associated ith a proportional (scalar) reduction of the original element stiffness matrices, equivalent to a scalar reduction of the material modulus, which characterises at Gauss point level. Finally, numerical examples for plane stress problem and plate bending problem are utilised to demonstrate the effectiveness of the proposed approach.

Two-Time Scale Control of Flexible Structures

In this paper, a direct iteration method is presented for two-time scale decomposition of flexible structures. This direct eigenspace approach has less computation burden than the eigenvector approach. It is also a canonical transformation to keep the equation symmetry and has also explicit inverse so that the input and output matrices of decoupled model with the same sensor and actor as the original system can be easily obtained.