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 recent papers, Surana et al presented
internal polar non-classical Continuum theory in which velocity gradient tensor
in its entirety was incorporated in the conservation and balance laws Thus,
this theory incorporated symmetric part of the velocity gradient tensor (as
done in classical theories) as well as skew symmetric part representing varying
internal rotation rates between material points which when resisted by
deforming continua result in dissipation (and/or storage) of mechanical work
This physics referred as internal polar physics is neglected in classical
continuum theories but can be quite significant for some materials In another
recent paper Surana et al presented ordered rate constitutive theories for
internal polar non-classical fluent continua without memory derived using
deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to
orders n and Cauchy moment tensor and its conjugate symmetric part of the first
convected derivative of the rotation gradient tensor In this constitutive
theory higher order convected derivatives of the symmetric part of the rotation
gradient tensor are assumed not to contribute to dissipation Secondly, the
skew symmetric part of the velocity gradient tensor is used as rotation rates
to determine rate of rotation gradient tensor This is an approximation to true
convected time derivatives of the rotation gradient tensor The resulting
constitutive theory: (1) is incomplete as it neglects the second and higher
order convected time derivatives of the symmetric part of the rotation gradient
tensor; (2) first convected derivative of the symmetric part of the rotation
gradient tensor as used by Surana et al is only approximate; (3) has
inconsistent treatment of dissipation due to Cauchy moment tensor when compared
with the dissipation mechanism due to deviatoric part of symmetric Cauchy
stress tensor in which convected time derivatives of up to order n are
considered in the theory The purpose of this paper is to present ordered rate
constitutive theories for deviatoric Cauchy strain tensor, moment tensor and
heat vector for thermofluids without memory in which convected time derivatives
of strain tensors up to order n are conjugate with the Cauchy stress tensor and
the convected time derivatives of the symmetric part of the rotation gradient
tensor up to orders 1n are conjugate with the moment tensor Conservation and
balance laws are used to determine the choice of dependent variables in the
constitutive theories: Helmholtz free energy density Φ, entropy density η,
Cauchy stress tensor, moment tensor and heat vector Stress tensor is
decomposed into symmetric and skew symmetric parts and the symmetric part of
the stress tensor and the moment tensor are further decomposed into equilibrium
and deviatoric tensors It is established through conjugate pairs in entropy
inequality that the constitutive theories only need to be derived for symmetric
stress tensor, moment tensor and heat vector Density in the current
configuration, convected time derivatives of the strain tensor up to order n,
convected time derivatives of the symmetric part of the rotation gradient
tensor up to orders 1n, temperature gradient tensor and temperature are
considered as argument tensors of all dependent variables in the constitutive
theories based on entropy inequality and principle of equipresence The
constitutive theories are derived in contravariant and covariant bases as well
as using Jaumann rates The nth and 1nth order rate constitutive theories for
internal polar non-classical thermofluids without memory are specialized for n
= 1 and 1n = 1 to demonstrate fundamental differences in the constitutive
theories presented here and those used presently for classical thermofluids
without memory and those published by Surana et al for internal polar
non-classical incompressible thermofluids

/pdf/rate-constitutive-theories-of-orders-n-and-1n-for-internal-p3i3x68xxq.pdf

Rate Constitutive Theories of Orders n and 1n for Internal Polar Non-Classical Thermofluids without Memory

On a mixed finite element model for large deformation analysis of elastic solids

The paper presents mathematical details of the finite element processes using the Galerkin method with weak form and least square processes for 1-D Helmholtz equation with Robin boundary condition in h,p,k framework. The concepts of variational consistency (VC) and variational inconsistency (VIC) are discussed. It is shown that Galerkin method with or without weak form is variationally inconsistent (VIC). The VIC of the Galerkin method is due to non-zero wave number (κ term) as well as Robin boundary condition. These two aspects of VIC of the integral forms and their consequences are investigated individually as well as jointly. It is shown that the integral forms yield non-symmetric functional B(.,.) and hence the possibility of complex basis for the coefficient matrix for some choices of h, p and k, which may lead to spurious or oscillatory non-physical numerical solutions. It is demonstrated that the variational consistency of the Galerkin method or galerkin method with weak form cannot be restored thr...

h, p, k Least Squares Finite Element Processes for 1-D Helmholtz Equation

The layerwise theory of Reddy is used to study the low velocity impact response of laminated plates. Forced-vibration analysis is developed by the modal superposition technique. Six different models are introduced for representation of the impact pressure distribution. The first five models, in which the contact area is assumed to be known, result in a nonlinear integral equation similar to the one obtained by Timoshenko in 1913. The resulting nonlinear integral equation is discretised using a time-element scheme. Two different interpolation functions, namely: (i) Lagrangian and (ii) Hermite, are used to express the impact force. The Hermitian polynomial-based representation, obviously more sophisticated, is introduced to verify the Lagrangian-based representation. Due to its modular nature the present numerical technique is preferable to the existing numerical methods in the literature. The final loading model, in which the time dependence of the contact area is taken into account according to the Hertzian contact law, resulted in a relatively more complicated but more realistic, nonlinear integral equation. The analytical developments concerning this model are all new and are reported for the first time in this paper. Also a simple, but accurate, numerical technique is developed for solving our new nonlinear integral equation which results in the time-history of the impact force. Our numerical results are first tested with a series of existing example problems. Then a detailed study concerning all the response quantities, including the in-plane and interlaminar stresses, is carried out for symmetric and antisymmetric cross-ply laminates and important conclusions are reached concerning the usefulness and accuracy of the various plate theories.

/pdf/forced-vibration-and-low-velocity-impact-of-laminated-5ilif04gb8.pdf

Forced vibration and low-velocity impact of laminated composite plates

The nonlinear response of laminated composite structures subjected to thermal loads is investigated. Analysis is performed using a refined theory and an associated finite element model for geometrically nonlinear analysis of laminated composite shell structures. The model is based on a third-order displacement field which accounts for both transverse shear and transverse normal deformations. Numerical studies of simply-supported plates and cylindrical panels indicate that when the panels are free to expand or contract in the transverse direction, the predicted critical buckling temperatures do not depend significantly upon whether or not transverse normal deformations are explicitly accounted for in the analysis model. However, the critical buckling temperatures are strongly dependent upon whether or not the transverse normal deformations are restrained along the boundaries of the panels.

J. N. Reddy

Papers

Rate Constitutive Theories of Orders n and 1n for Internal Polar Non-Classical Thermofluids without Memory

On a mixed finite element model for large deformation analysis of elastic solids

h, p, k Least Squares Finite Element Processes for 1-D Helmholtz Equation

Forced vibration and low-velocity impact of laminated composite plates

Thermomechanical postbuckling analysis of laminated composite shells