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 finite element models based on the weak-form Galerkin formulation the equilibrium of forces is satisfied at the computational nodes. In general, however, equilibrium is not satisfied within an element and across inter-element boundaries. Through geometrical considerations of the governing equations, a spectral element method is presented, which satisfies force equilibrium locally as well as globally. The method discretizes displacements at points and forces over surfaces. In this way the force equilibrium equations can be identically satisfied independent of the size or shape of the grid. Since the forces are discretized at surfaces there is a perfect force balance at the boundaries between elements. This also makes the method very robust for even highly deformed meshes, which is illustrated through numerical examples.

Exact Force Equilibrium in Linear Elasticity

In this paper, a finite element model for the nonlinear analysis of laminated shell structures and through-thickness functionally graded shells is presented. A tensor-based finite element formulation is presented to describe the deformation and constitutive laws of a shell in a natural and simple way by using curvilinear coordinates. In addition, a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking; no mixed interpolations are employed. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and, therefore, 3D constitutive equations are utilized. Numerical comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composite plates and shells as well as functionally graded plates and shells are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation in shells.

Nonlinear Analysis of Composite and FGM Shells using Tensor-Based Shell Finite Elements

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation , and/or shear strain , as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.

http://jsm.iau-arak.ac.ir/article_539692_7de7e45c949e258c87bffbd8a599183e.pdf

Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations

http://link.springer.com/content/pdf/10.1007/978-3-642-83535-3_2.pdf

Variational Formulations and Methods

In this chapter, we will demonstrate how the SMA wires and springs are actuated and the way a given stroke is achieved by means of temperature changes.

J. N. Reddy

Papers

Exact Force Equilibrium in Linear Elasticity

Nonlinear Analysis of Composite and FGM Shells using Tensor-Based Shell Finite Elements

Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations

Variational Formulations and Methods

Graphical Description of Temperature Controlled Actuation of SMA Wires