Plates on Elastic Foundation

Analysis of rectangular plates resting on a Winkler-type, one-parameter foundation is studied. The finite element method is applied and a 12-degree-of-freedom, nonconforming rectangular plate element is adopted. Based on shape functions of the plate element, an energy approach is used to derive a closed-form, 12-by-12, consistent foundation stiffness matrix for a rectangular plate on an elastic subgrade. A commonly used method of modeling structural elements on an elastic foundation is the application of discrete springs at the element nodes. The model developed in this paper is compared with the discrete spring model and the convergence of both models is discussed. The convergence of the models is compared with the well-known classical solution of plates on elastic foundation developed in the 1950s. Both models show good convergence to the classical solution. The continuous subgrade response model converges in a manner more consistent with the flexibility of the plate element.

Parallel computing concepts and methods for floquet analysis of helicopter trim and stability

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive, Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors, The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated, For illustration, flap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-state three-dimensional wake model are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses, Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.

Stability of laminated composite plates with cut-outs

Critical buckling loads of laminated fibre-reinforced plastic square panels have been obtained using the finite element method. Various boundary conditions, lay-up details, fibre orientations, cut-out sizes are considered. A 36 degrees of freedom triangular element, based on the classical lamination theory (CLT) has been used for the analysis. The performance of this element is validated by comparing results with some of those available in literature. New results have been given for several cases of boundary conditions for [0°/ ± 45°/90°]s laminates. The effect of fibre-orientation in the ply on the buckling loads has been investigated by considering [±?]6s laminates.

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 degrees/0 degrees/-45 degrees/90 degrees](s) circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.

On boundedness and parallel to center dot parallel to(p) continuity of second quantisation

in this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map.

Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays

A symmetrizer of a nonsymmetric matrix A is the symmetric matrix X that satisfies the equation XA = A(t)X, where t indicates the transpose. A symmetrizer is useful in converting a nonsymmetric eigenvalue problem into a symmetric one which is relatively easy to solve and finds applications in stability problems in control theory and in the study of general matrices. Three designs based on VLSI parallel processor arrays are presented to compute a symmetrizer of a lower Hessenberg matrix. Their scope is discussed. The first one is the Leiserson systolic design while the remaining two, viz., the double pipe design and the fitted diagonal design are the derived versions of the first design with improved performance.

Lamination-dependent shear deformation models for bending of angle-ply laminated plates

Lamination-dependent shear corrective terms in the analysis of bending of laminated plates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses by using CLPT inplane stresses in the two in-plane equilibrium equations of elasticity in each ply. In the development of a general model for angle-ply laminated plates, special cases like cylindrical bending of laminates in either direction, symmetric laminates, cross-ply laminates, antisymmetric angle-ply laminates, homogeneous plates are taken into consideration. Adding these corrective terms to the assumed displacements in (i) Classical Laminate Plate Theory (CLPT) and (ii) Classical Laminate Shear Deformation Theory (CLSDT), two new refined lamination-dependent shear deformation models are developed. Closed form solutions from these models are obtained for antisymmetric angle-ply laminates under sinusoidal load for a type of simply supported boundary conditions. Results obtained from the present models and also from Ren's model (1987) are compared with each other.

Large deformation finite element analysis of laminated circular composite plates

A 48 d.o.f., four-noded quadrilateral laminated composite shell finite element is particularised to a sector finite element and is used for the large deformation analysis of circular composite laminated plates. The strain-displacement relationships for the sector element are obtained by reducing those of the quadrilateral shell finite element by substituting proper values for the geometric parameters. Subsequently, the linear and tangent stiffness matrices are formulated using conventional methods. The Newton-Raphson method is employed as the nonlinear solution technique. The computer code developed is validated by solving an isotropic case for which results are available in the literature. The method is then applied to solve problems of cylindrically orthotropic circular plates. Some of the results of cylindrically orthotropic case are compared with those available in the literature. Subsequently, application is made to the case of laminated composite circular plates having different lay-up schemes. The computer code can handle symmetric/unsymmetric lay-up schemes. The large displacement analysis is useful in estimating the damage in composite plates caused by low-velocity impact.

Modeling of the cooling process on the runout table of a hot strip mill - A parallel approach

This paper deals with the development of a new model for the cooling process on the runout table of hot strip mills, The suitability of different numerical methods for the solution of the proposed model equation from the point of view of accuracy and computation time are studied, Parallel solutions for the model equation are proposed.

Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Parallel implementation of alternate quadrant interlocking factorisation method on star topology

This paper discusses the parallel implementation of the solution of a set of linear equations using the Alternative Quadrant Interlocking Factorisation Methods (AQIF), on a star topology. Both the AQIF and LU decomposition methods are mapped onto star topology on an IBM SP2 system, with MPI as the internode communicator. Performance parameters such as speedup, efficiency have been obtained through experimental and theoretical means. The studies demonstrate (i) a mismatch of 15% between the theoretical and experimental results, (ii) scalability of the AQIF algorithm, and (iii) faster executing AQIF algorithm.

Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computations

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.