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

Numerical Initial Value Problems in Ordinary Differential Equations

1.Introduction to Composite Materials 2. Macrochemical Behavior of a Lamina 3.Micromechanical Behavior of a Lamina 4.Macromechanical Behavior of a Laminate 5.Bending, Buckling, and Vibration of Laminated Plates 6.Other Analysis and Behavior Topics 7.Introduction to Design of Composite Structures Appendix A.Matrices and Tensors Appendix B.Maxima and Minima of Functions of a Single Variable Appendix C.Typical Stress-Strain Curves Appendix D.Governing Equations for Beam Equilibrium and Plate Equilibrium, Buckling, and Vibration Index

/pdf/mechanics-of-composite-materials-4uyw5i9ck8.pdf

Mechanics of composite materials

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

Novel displacement gradient boundary element method for elastic stress analysis with high accuracy

Nonlinear elastodynamics problems are approached from the point of view of a mixed variational principle. It is shown that four different functionals lead to different formulations of the problem with different independent fields. One of the functionals is specialized to the case of spatial beams undergoing large deformations, and small strains. The extension of these functionals to the case in which kinematic constraints are presented leads to the useful concept of dual constraints, which can be advantageously employed in treating problems involving contact, impact, and changing topology.

Mixed variational principles in space and time for elastodynamics analysis

The prediction of transient response of structures, in the form of traveling waves, is very important for controlling the dynamic behavior of structures. It is well known that the standard semi-discrete form of the finite element method is not suitable for predicting the wave propagation, due to the inherent dispersion involved. In this paper, an application of space-time finite element method to the wave propagation problem is discussed. The main concerns in such problems consist of developing a consistent and stable scheme and also of capturing a shock wave, without wiggling. We discuss, at first, a weak form of the wave propagation problem, taking into account the jump condition associated with velocity and stress. A mixed finite element formulation plays an important role in evaluating the velocity explicitly. The application of present formulation to the linear wave equation shows that the present numerical results at the discontinuity give the mean values of jump. In the case of flexural wave propagations in Timoshenko beam, the present method captures the wave front easily rather than the semi-discrete method.

Analysis of Traveling Wave Responses of Structures

A three-dimensional analysis of cracks in adhesively bonded laminates, with debonding around the crack, is presented. The three-dimensional finite element method is based on a hybrid-stress procedure. Effects of the following parametricvariations are studied: (i) relative thicknesses of adhesives, (ii) relative material properties of adhesives and adherends, (iii) ratio of flaw length, to laminate characteristic dimensions, and (iv) shape of debonded region.

Analysis of cracks in adhesively bonded metallic laminates by a 3-dimensional assumed stress hybrid fem.

The Finite element alternating method is applied to obtain the stress intensity factors of collinear multiple cracks in a thin isotropic plate subjected to bending moment. The necessary analytical solutions are obtained by using the complex stress function method given by Muskhelishvili and Savin. In order to verify the efficiency of the proposed method, several example problems are solved and compared with the published results.

Analysis of a cracked thin isotropic plate subjected to bending moment by using FEAM

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