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

Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory

Present investigation is concerned with the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions. The analysis is based on the classical and first order shear deformation beam theories. Material properties of the beam vary continuously in the thickness direction according to the power-law exponent form. Trial functions denoting the displacement components of the cross-sections of the beam are expressed in simple algebraic polynomial forms. The governing equations are obtained by means of Rayleigh–Ritz method. The objective is to study the effects of constituent volume fractions, slenderness ratios and the beam theories on the natural frequencies. To validate the present analysis, comparison studies are also carried out with the available results from the existing literature.

Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method

Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams are studied through a finite element approach. The exact shape functions for uniform homogeneous Timoshenko beam elements are used to formulate the proposed element. The accuracy of the present element is considerably improved by considering the exact variations of cross-sectional profile and mechanical properties in the evaluation of the structural matrices. Carrying out several numerical examples, the convergence of the method is verified and the effects of taper ratio, elastic constraint, attached mass and the material non-homogeneity on the natural frequencies and critical buckling load are investigated.

Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions

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Introduction To Statistical Thermodynamics

Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finiteelement method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

https://downloads.hindawi.com/journals/sv/2011/591716.pdf

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Nano-scale investigation of elastic properties of hydrated cement paste constituents using molecular dynamics simulations

In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.

Shahin Hajilar

Papers

Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Nano-scale investigation of elastic properties of hydrated cement paste constituents using molecular dynamics simulations

A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams

Mechanical failure mechanisms of hydrated products of tricalcium aluminate: A reactive molecular dynamics study