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

Finite-element solutions of a number of one-dimensional linear and nonlinear (nonsingular) integral equations arising in radiative heat transfer and boundarylayer theory are presented.

Finite-Element Solution of Integral Equations Arising in Radiative Heat Transfer and Laminar Boundary-Layer Theory

A note on mixed variational principles for initial-value problems

Assessment of the effect of negative Poisson’s ratio on the thermal postbuckling of temperature dependent FG-GRMMC laminated cylindrical shells

In this article an efficient 3-D continuum damage mechanics formulation for composite laminates and its implementation into a finite element model that is based on the first order shear deformation theory of laminates are described. In the damage formulation each composite ply is treated as a homogeneous orthotropic material that can exhibit orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. This type of damage is efficiently described by a symmetric second order tensor field that serves as an evolving internal variable within the framework of irreversible thermodynamics. The damage tensor is continuous within each material ply of a given element, but can be discontinuous across material layer boundaries and inter-element boundaries. The resulting finite element formulation is shown to be robust, stable and efficient for the simulation of progressive damage and global failures in large-scale composite laminate problems. Numerical ex...

An Efficient Continuum Damage Model and its Application to Shear Deformable Laminated Plates

A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler–Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler–Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.

J. N. Reddy

Papers

Finite-Element Solution of Integral Equations Arising in Radiative Heat Transfer and Laminar Boundary-Layer Theory

A note on mixed variational principles for initial-value problems

Assessment of the effect of negative Poisson’s ratio on the thermal postbuckling of temperature dependent FG-GRMMC laminated cylindrical shells

An Efficient Continuum Damage Model and its Application to Shear Deformable Laminated Plates

A discrete Lagrangian based direct approach to macroscopic modelling