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

: Geometrically nonlinear analyses of BCM structures; experimental investigations of BCMs and structures; analyses of structures made of nonlinear composite materials, and new structural analyses. The research program was reported in a series of thirty-seven technical reports (including the present one) and sixty-eight conference papers and journal articles, all of which are listed herein. (Author)

Nonlinear Analysis of Laminated, Bimodular Composite Material Structures.

We look for an enhancement of the correspondence model of peridynamics with a view to eliminating the zero-energy deformation modes. Since the non-local integral definition of the deformation gradient underlies the problem, we initially look for a remedy by introducing a class of localizing corrections to the integral. Since the strategy is found to afford only a reduction, and not complete elimination, of the oscillatory zero-energy deformation, we propose in the sequel an alternative approach based on the notion of sub-horizons. A most useful feature of the last proposal is that the setup, whilst providing the solution with the necessary stability, deviates only marginally from the original correspondence formulation. We also undertake a set of numerical simulations that attest to the remarkable efficacy of the sub-horizon based methodology.

A simple alteration of the peridynamics correspondence principle to eliminate zero-energy deformation

Finite element analysis of viscous incompressible flows using primitive variables

This paper addresses bending of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elastic theory. In the present model, the equations of motion are derived by expanding the displacement field using the Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.

A semi-analytical finite element model for the analysis of piezolaminated cylindrical shells

Two global/local finite element modeling procedures are integrated to permit the analysis of localized three-dimensional affects in laminated composite plates with bonded or embedded actuators. The first technique concerns the use of variable kinematic finite elements which are elements that contain several different types of assumed displacement fields. By choosing appropriate terms from the composite displacement field, an entire array of elements with different levels of kinematic complexity can be formed. The different elements can be conveniently connected together in a single domain for global/local analysis. The second technique concerns the use of finite element mesh superposition in which an independent overlay mesh is superimposed on a global mesh to provide localized refinement for regions of interest regardless of the original global mesh topology. Integration of these two ideas yields a very robust, economical analysis tool for global/local analysis of composite laminates.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

J. N. Reddy

Papers

Nonlinear Analysis of Laminated, Bimodular Composite Material Structures.

A simple alteration of the peridynamics correspondence principle to eliminate zero-energy deformation

Finite element analysis of viscous incompressible flows using primitive variables

A semi-analytical finite element model for the analysis of piezolaminated cylindrical shells

Modeling of actuators in laminated composite structures