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

An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.

Exact Solutions of Moderately Thick Laminated Shells

Theories and computational models for composite laminates

Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates

Preface 1.General Introduction and Preliminaries 2.Virtual Work Principles and Solution Methods 3.Theory and Analysis of Euler-Bernoulli Beams 4.Theory and Analysis of Timoshenko Beams 5.The Classical Plate Theory 6.The First Order Shear Deformation Theory 7.Variational Solutions of Plates 8.Finite Element Analysis of Beams and Plates 9.Refined Theories of Plates 10.Nonlinear Analysis of Beams and Plates Subject Index

Theory and analysis of elastic plates

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

J. N. Reddy

Papers

Exact Solutions of Moderately Thick Laminated Shells

Theories and computational models for composite laminates

Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates

Theory and analysis of elastic plates

Modelling of thick composites using a layerwise laminate theory