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Two efficient computational procedures are presented for generating the global approximation vectors used in conjunction with the reduction methods for the large‐deflection non‐linear analysis of symmetric structures with unsymmetric boundary conditions. Both procedures are based on restructuring the governing equations for each of the unsymmetric global approximation vectors to delineate the different contributions to the symmetric and antisymmetric components of this vector. In the first procedure the unsymmetric global approximation vectors are approximated by linear combinations of symmetric and antisymmetric modes, which are generated by using the finite element method. The amplitudes of these modes are computed by using the classical Rayleigh‐Ritz technique. The second procedure is based on using a preconditioned conjugate gradient (PCG) technique for generating the global approximation vectors, and selecting the preconditioning matrix to be the matrix associated with the symmetric response. In both procedures the size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions. The similarities between the two procedures are identified, and their effectiveness is demonstrated by means of two numerical examples of large‐deflection, non‐linear static problems of shells.

The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

When the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric matrices can be obtained by finding the least Frobenius norm generalized centro‐symmetric and central anti‐symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous‐time algebraic Lyapunov equations (GCALE).

By the algorithms, the solvability of the general coupled matrix equations over generalized centro‐symmetric and central anti‐symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods.

A computational procedure is presented for the efficient non‐linear dynamic analysis of quasi‐symmetric structures. The procedure is based on approximating the unsymmetric response vectors, at each time step, by a linear combination of symmetric and antisymmetric vectors, each obtained using approximately half the degrees of freedom of the original model. A mixed formulation is used with the fundamental unknowns consisting of the internal forces (stress resultants), generalized displacements and velocity components. The spatial discretization is done by using the finite element method, and the governing semi‐discrete finite element equations are cast in the form of first‐order non‐linear ordinary differential equations. The temporal integration is performed by using implicit multistep integration operators. The resulting non‐linear algebraic equations, at each time step, are solved by using iterative techniques. The three key elements of the proposed procedure are: (a) use of mixed finite element models with independent shape functions for the stress resultants, generalized displacements, and velocity components and with the stress resultants allowed to be discontinuous at interelement boundaries; (b) operator splitting, or restructuring of the governing discrete equations of the structure to delineate the contributions to the symmetric and antisymmetric vectors constituting the response; and (c) use of a two‐level iterative process (with nested iteration loops) to generate the symmetric and antisymmetric components of the response vectors at each time step. The top‐ and bottom‐level iterations (outer and inner iterative loops) are performed by using the Newton—Raphson and the preconditioned conjugate gradient (PCG) techniques, respectively. The effectiveness of the proposed strategy is demonstrated by means of a numerical example and the potential of the strategy for solving more complex non‐linear problems is discussed.

This study aims to investigate the relationship between trust and performance in international joint ventures (IJVs) with the moderating effects of the structural mechanisms from transaction cost approach.

Using web-survey, data are collected from 89 IJVs of Northern European firms in Asia, Europe and America. Empirical data are analyzed with structural equation modeling and estimates moderating effects of symmetric dependence, symmetric equity share and resource complementarity.

The findings offer some interesting insights for transaction cost and the social exchange theory. This study demonstrates that a symmetric equity share between IJV partners does not moderate the trust–performance relationship, while a symmetric dependence and resource complementarity between partners effect positively. Therefore, trust takes on greater importance in enhancing IJV performance under symmetric dependence and resource complementarity and symmetric equity share between IJV partners deprecates the importance of equity distribution.

A symmetric dependence prevents the deceit from either partner in trusting relationships. Further, a trustful relationship enhances IJV performance regardless of the equity share in IJVs. IJVs with asymmetric equity share can also be successful, provided that IJV partners develop inter-partner trust.

The extant research has not examined how the trust–performance relationship is contingent on structural mechanisms of IJVs that transaction cost economics deem necessary to prevent opportunistic behavior. Three structural mechanisms of symmetric dependence, symmetric equity share and resource complementarity moderate the trust–performance relationship in IJVs.

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is its slow convergence, even when it is used in conjunction with acceleration techniques. The Newton‐Raphson method has a rapid convergence rate, but its implementation resorts to non‐symmetric linear solvers, and hence the memory requirement may be high. The purpose of this paper is to develop more advanced solution techniques which may overcome the above problems associated with the initial stiffness method and the Newton‐Raphson method.

In this work, the accelerated symmetric stiffness matrix methods, which cover the accelerated initial stiffness methods as special cases, are proposed for non‐associated plasticity. Within the computational framework for the accelerated symmetric stiffness matrix techniques, some symmetric stiffness matrix candidates are investigated and evaluated.

Numerical results indicate that for the accelerated symmetric stiffness methods, the elasto‐plastic constitutive matrix, which is constructed by mapping the yield surface of the equivalent material to the plastic potential surface, appears to be appealing. Even when combined with the Krylov iterative solver using a loose convergence criterion, they may still provide good nonlinear convergence rates.

Compared to the work by Sloan et al., the novelty of this study is that a symmetric stiffness matrix is proposed to be used in conjunction with acceleration schemes and it is shown to be more appealing; it is assembled from the elasto‐plastic constitutive matrix by mapping the yield surface of the equivalent material to the plastic potential surface. The advantage of combining the proposed accelerated symmetric stiffness techniques with the Krylov subspace iterative methods for large‐scale applications is also emphasized.

Defines and investigates fuzzy symmetric functions with don't‐care conditions and most‐unsymmetric functions. Represents and illustrates by examples algorithms for finding the grade of membership function and the number of most unsymmetric functions. Also presents applications to function representation, data reduction and error correction. The results may have useful applications to fuzzy logics, finding most‐unsymmetric images, fuzzy neural networks and related areas.

The propagation of circular crested waves in a fluid saturated incompressible porous plate is analyzed. The frequency equations, for symmetric and anti‐symmetric waves, connecting the phase velocity with wave number are derived. At short wave length limits the frequency equations for symmetric and antisymmetric waves in a stress free plate reduce to Rayleigh type surface wave frequency equation and the finite thickness plate appears as a semi‐infinite medium. The results at various steps are compared with the corresponding results of classical theory and finally the variations of phase velocity, attenuation coefficient with wave number and displacements amplitudes with distance from the boundary of the plate is presented graphically and discussed.

The purpose of this paper is to demonstrate new properties of continuous‐ and discrete‐time dynamical systems.

First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown.

The main result of the paper is a new theorem regarding new properties of continuous‐ and discrete‐time dynamical systems.

The present study provides a starting point for further research on the differences between continuous‐ and discrete‐time dynamical systems. This work builds on the definition of spatial symmetry.

The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous‐time dynamical systems by discrete‐time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise.

This paper offers contributions to the broader discussion of differences between continuous‐ and discrete‐time dynamical systems. In particular, the paper supports the statement that many discrete‐time processes cannot be embedded into continuous ones.

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

A computational procedure is presented for the re‐analysis of large unsymmetric structural systems. The procedure is based on a novel partitioning strategy in which the responses of both the original and modified structures are approximated by linear combinations of symmetric and antisymmetric response vectors (or modes), each obtained by using a fraction of the degree of freedom of the finite element model of the structure. The other key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or restructuring of the governing finite element equations to delineate the symmetric and antisymmetric vectors constituting the responses of the original and modified structures; and (c) a stable and efficient iterative process for generating the response of the modified structure. The re‐analysis procedure is applied to linear static analysis of framed structures. Design modifications consisted of removing members resulting in topologically unsymmetric structures. The potential of the procedure on multiprocessor computers is discussed and its effectiveness is demonstrated by means of two numerical examples.