J. N. Reddy

Bio: J. N. Reddy is an academic researcher from Texas A&M University. The author has contributed to research in topics: Finite element method & Plate theory. The author has an hindex of 106, co-authored 926 publications receiving 66940 citations. Previous affiliations of J. N. Reddy include Instituto Superior Técnico & National University of Singapore.

Large strained fracture of nearly incompressible hyperelastic materials: enhanced assumed strain methods and energy decomposition

Abstract: Tracking crack propagation at large strains of hyperelastic solids is a challenging task due to the high nonlinearity, nearly incompressibility and ordered tendency in microstructure of the rubbery material under stretch. On the basis of the diffusive crack model, this work presents a new phase-field model by combining the strain energy decomposition and the enhanced assumed strain method. The proposed fracture formulation is indeed Griffith's theory-based framework but further accounting for the coupled effects of the stretches, damage and incompressibility to predict the crack growth in both compressible and incompressible hyperelastic solids. There are three innovations contained in this study: (i) The developed phase-field framework is capable to capture the effect of hole collapse, which is an intrinsic phenomenon of hyperelastic material and difficult to be detected by the others. (ii) The developed energy decomposition method provides a reasonable description of the physical reality that the hyperelastic fracture is driven by the changes in the internal energy of the stretched molecular chains in the polymer network. This continuum description automatically distinguishes the strain energy that really contributes to crack growth at multiaxial stress states, reducing significantly the numerical instability caused by material softening. (iii) By introducing the assumed strain method to the present fracture scheme, the physical consistency of energy decomposition and the mathematical nonnegativeness of strain energy can be satisfied simultaneously for incompressible problem. We demonstrate the performance of the enhanced phase-field framework through representative examples and highlight the importance of positive deviatoric energy for incompressible problem by comparing with experiments and classical models.

Penalty finite element analysis of incompressible flows using element by element solution algorithms

Abstract: Finite element analysis of complex three-dimensional flows requires solution of a large system of algebraic equations. These equations are most often solved using direct methods, i.e., Gauss elimination method. However, for complex problems, direct methods demand prohibitively large CPU times and storage, thus making it difficult to solve these equations economically even on supercomputers. Iterative methods, on the other hand, do not require large storage and CPU times because the global system of equations are not formulated and factorized. These advantages over direct methods have revived the interest in iterative solvers. The element by element solvers using conjugate gradient methods have been used successfully for the solution of problems in fluid and solid mechanics and were shown to be advantageous over direct methods. In this paper we present an element by element algorithm for solution of incompressible flow problems using a penalty finite element model. The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved.

I and i

Abstract: 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 …

Fast parallel algorithms for short-range molecular dynamics

Abstract: 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.

Robot dynamics and control

Abstract: 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.

A Simple Higher-Order Theory for Laminated Composite Plates

Abstract: 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.