There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

From the Publisher:
This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.

Robot dynamics and control

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A Simple Higher-Order Theory for Laminated Composite Plates

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

A consistent third-order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed. The formulation has seven displacement functions and requires C 0 continuity in the displacement field. The exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate. A displacement finite element model is developed using Lagrange elements with higher-order interpolation polynomials. These elements preclude any effect of shear and membranes locking. Comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code.

Consistent Third-Order Shell Theory with Application to Composite Cylindrical Cylinders

Generalized beam theories accounting for von Kármán nonlinear strains with application to buckling

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators

A continuum-based, laminated, stiffened shell element is used to investigate the static, geometrically nonlinear response of composite shells. The element is developed from a three-dimensional continuum element based on the incremental, total Lagrangian formulation. The Newton-Raphson method or modified Riks method is used to trace the nonlinear equilibrium path. A number of sample problems of unstiffened and stiffened shells are presented to show the accuracy of the present element and to investigate the nonlinear response of laminated composite plates and shells. INITE-ELEMENT analyses of the large displacement the- ories are based on the principle of virtual work or the associated principle of stationary potential energy. Horrigmoe and Bergan1 presented classical variational principles for non- linear problems by considering incremental deformations of a continuum. A survey of various principles in incremental form in different reference configurations, such as the total Lagran- gian and updated Lagrangian formulations, is presented by Wiinderlich.2 In the total Lagrangian description, all static and kinematic variables are referred to the initial configura- tion. Finite-element models based on such formulations have been used in the analysis of arch and shell instability prob- lems.3'6 A special numerical technique must be adopted to trace the path of the load-deflection curve near the limit point (i.e., critical buckling load) and in the postbuckling region, because the stiffness matrix in the vicinity of the limit point is nearly singular, and the descending branch of the load-deflec- tion curve in the postbuckling region is characterized by a negative-definite stiffness matrix. Many methods have been proposed to solve limit-point problems. Among these are the simple methods of suppressing equilibrium iterations,7'8 the introduction of artificial spring,3 the displacement control method,7'8 and the "constant-arc-length method" of Riks. 11-12 Reviews of these most commonly used techniques are con- tained in Refs. 13 and 14. Among these methods, the modified Riks method appears to be the most effective in conjunction with the finite-element method. Many investigators11'15 have used this method in its original or modified form to determine the pre- and postbuckling behavior of various types of struc- tures such as arches, shells, and domes. In most of these works, only isotropic material was considered. Very few works of the nonlinear buckling analysis of laminated com- posite structures are reported in the literature.16 When solving the problems of shells with stiffeners by the finite-element method, a beam element whose displacement pattern is compatible with that of the shell is required. In analyzing eccentrically stiffened cylindrical shell, Kohnke and Schnobrich17 proposed a 16-deg-of-free dom (DOF) isotropic beam finite element that has displacements compatible with

J. N. Reddy

Papers

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

Consistent Third-Order Shell Theory with Application to Composite Cylindrical Cylinders

Generalized beam theories accounting for von Kármán nonlinear strains with application to buckling

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators

Continuum-based stiffened composite shell element for geometrically nonlinear analysis