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

In spite of the rather complex and hysteretic behavior of SMA components (wires and springs), and the complex changes that occur in their microstructures, the preliminary design of SMA wires and springs turns out to be reasonably simple provided we utilize their shape memory characteristics in specific ways. Designing SMA actuators requires defining actuation intervals (temperature profile), load levels and/or displacement outputs over its intended designed life. The alloy composition dictates the transformation temperatures and the component’s operating range. SMA components could be functional under load controlled or displacement controlled or simultaneous load and displacement controlled setups.

Case Studies in the Preliminary Design of SMA Actuators

This chapter is concerned with the numerical simulation of scratch deformation on a polymer substrate by a semispherical indenter. A commercial finite element (FE) package, ABAQUS®, is used to study elasto-plastic scratch behavior on polymer surfaces. The study provides insightful mechanistic information that can be correlated to surface deformation and damage using material parameters. Of notable significance is that the FE analysis approach can be used to conduct parametric studies on material and geometric parameters that aid the construction of a physics-based model for describing the scratch behavior of polymers.

Finite Element Modeling for Scratch Damage of Polymers

: This final technical report summarizes in a compact form the results of a two-year research program on the development of refined shear deformation theories of plates and shells, and their analytical solutions. The detailed results are reported in various reports and technical papers during the course of the project. A third-order, nonlinear shear deformation shell theory and finite element model that accounts for parabolic distribution of transverse shear stresses through thickness and the von Karman nonlinear strains was developed during an investigation sponsored by NASA Langley Research Center during the first year of this research. The most significant contributions of this research are: 1. The development of analytical solutions of the linear theory for various boundary conditions. The space-time concept is used to develop such solutions. 2. The development of finite element models for first-ply and post-first-ply failure analysis.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA184436&Location=U2&doc=GetTRDoc.pdf

A Refined Nonlinear Analysis of Laminated Composite Plates and Shells.

This paper has a twofold objective: to present (a) a computational model for the finite deformation analysis of shell structures and (b) the development of mathematical model of biological cells based on homogenization techniques In the first part, we present a finite element formulation which describes a refined shell theory in a natural and simple way using curvilinear coordinates The first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description This approach takes in-to account thickness changes and, therefore, 3D constitutive equations are utilized In addition, we utilize the equal order, spectral/hp approximations for all variables in the finite element model to avoid membrane and shear Numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic, laminated composites, as well as functionally graded shells are presented In the second part, we present a mechanical model for a generalized biological cell, which includes the features of major cell types The properties of biological materials are closely related to their internal molecular structure, and therefore require a micro-constituent based mathematical model to determine its macroscopic properties In this work, the mathematical model is based on the actin fiber concentration, which could be used for the determination of mechanical properties of normal and diseased cells Numerical results obtained with the present continuum model are compared with experimental results and a very good agreement is found

Numerical Modeling of Complex Structures: Shells and Biological Cells

Given the complex nonlinear nature of SMA responses, understanding their coupled thermomechanical responses of different components has been of significant interest for both researchers and application developers.

J. N. Reddy

Papers

Case Studies in the Preliminary Design of SMA Actuators

Finite Element Modeling for Scratch Damage of Polymers

A Refined Nonlinear Analysis of Laminated Composite Plates and Shells.

Numerical Modeling of Complex Structures: Shells and Biological Cells

Factors Influencing Design of SMA Actuators