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

https://link-springer-com-443.webvpn.jmu.edu.cn/content/pdf/10.1007%2F978-3-030-10475-7_37-1.pdf

Numerical Methods, Finite Element

Variable Thickness Structures

A four-field mixed variational principle is proposed for large deformation analysis of Kirchhoff rods with the lowest order C mixed FE approximations. The core idea behind the approach is to introduce a one-parameter family of points (the centerline) and a separate one-parameter family of orthonormal frames (the Cartan moving frame) that are specified independently. The curvature and torsion of the curve are then related to the relative rotation of neighboring frames. The relationship between the frame and the centerline is then enforced at the solution step using a Lagrange multiplier (which plays the role of section force). Well known frames like the Frenet-Serret are defined only using the centerline, which demands higher-order smoothness for the centerline approximation. Decoupling the frame from the position vector of the base curve leads to a description of torsion and curvature that is independent of the position information, thus allowing for simpler interpolations. This approach is then cast in the language of exterior calculus. In this framework, the strain energy may be interpreted as a differential form leading to the natural force-displacement (velocity) pairing. The four-field mixed variational principle we propose has frame, differential forms, and position vector as input arguments. While the position vector is interpolated linearly, the frames are interpolated as piecewise geodesics on the rotation group. Similarly, consistent interpolation schemes are also adopted to obtain finite dimensional approximations for the differential forms appearing in the mixed functional. Using these discrete approximations, a discrete mixed variational principle is laid out which is then numerically extremized. The discrete approximation is then applied to a few benchmark problems. Vis-á-vis most available approaches, our numerical studies reveal an impressive performance of the proposed method without numerical instabilities or locking.

A novel four-field mixed variational approach to Kirchhoff rods implemented with finite element exterior calculus

A novel conduction heating apparatus that combines thermal loading with large deflection bending is introduced, and its effectiveness for thermo-mechanical stress analysis was investigated. By clamping composite specimens (M40J/PMR-II-50, [0,90]s , a uni-tape cross-ply) on the radial sides of half cylinders having two different radii (78.74mm and 37.96mm), three different in-plane strains including a no strain condition were applied to the composites. Three different thermal loading experiments, 1) 23°C to −196°C to 250°C, 2) 23°C to 250°C, and 3) 23°C to −196°C were performed as a function of mechanical in-plane strain levels. The apparatus was excellent enough to generate cracks related to the in-plane stresses (or strains) on plies. The quadratic failure criteria solution based on the thermal residual stresses shows a good agreement with the experimental results at low temperatures, but does not supply a good agreement at high temperatures. A weak adhesion of fiber/matrix interface at high temperatures (250°C) might cause the de-bonding at the interface and subsequent exposure to −196°C caused the intensive crack propagation.© 2005 ASME

Thermo-Mechanical Analysis of Composites Under Combined Conduction Heating and Large Deflection Bending

: Work performed during the third year of the Grant: (1) Preliminary research on fluid-solid interaction, development of mathematical models, computational methodology in hpk framework. (2) Preliminary research towards development of concepts for a priori and a posteriori error estimation in hpk mathematical and computational framework. (3) Re-discretizations, moving meshes and solution mapping strategies and associated computational infrastructures for BVPs and IVPs in hpk framework (Appendix A contains technical report on this work).

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA465662&Location=U2&doc=GetTRDoc.pdf

J. N. Reddy

Papers

Numerical Methods, Finite Element

Variable Thickness Structures

A novel four-field mixed variational approach to Kirchhoff rods implemented with finite element exterior calculus

Thermo-Mechanical Analysis of Composites Under Combined Conduction Heating and Large Deflection Bending

kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP