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.

Penalty finite element analysis of free surface flows of power-law fluids

Abstract: The penalty function method is used to formulate the finite element model of the free surface flows of incompressible, viscous, power-law fluids in plane and axisymmetric situations. Two different procedures of obtaining the free surface are presented, and application of the present finite element model to die-swell problems is discussed. The numerical results are compared with available experimental data and numerical results obtained by others.

Nonlinear Analysis of Microbeam under Electrostatic Loading

Abstract: In this study we investigated the behavior of a microbeam subjected to electrostatic loading. Two devices, namely, a tungsten microtweezer and a clamped-clamped beam which is part of a micro-electromechanical system (MEMS), are used. The deflection of beams is studied for various cases of loading, i.e., constant loading, linear loading and nonlinear loading. Both linear and non-linear behavior of the microbeams are studied. The Euler-Bernoulli beam theory as well as the Timoshenko beam theory is used to study deflection of the beams. Governing equations are solved for each case by two different approaches. Simple cases of the governing equations are solved analytically. The nonlinear differential equation is solved by the finite element method. Results for different cases are compared and discussed.

Constitutive theories for thermoelastic solids in Lagrangian description using Gibbs potential

Abstract: This paper presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation of mass, balance of momenta and the energy equation are independent of the constitution of the matter, the second law of thermodynamics, that is, entropy inequality, must form the basis for all constitutive theories of the deforming matter to ensure thermodynamic equilibrium during the evolution (Surana and Reddy in Continuum mechanics, 2012; Eringen in Nonlinear theory of continuous media. McGraw-Hill, New York, 1962). The entropy inequality expressed in terms of Helmholtz free energy is recast in terms of Gibbs potential. The conditions resulting from the entropy inequality expressed in terms of Gibbs potential permit the derivation of the constitutive theory for the strain tensor in terms of the conjugate stress tensor and the constitutive theory for the heat vector. In the work presented here, it is shown that using the conditions resulting from the entropy inequality, the constitutive theory for the strain tensor can be derived using three different approaches: (i) assuming the Gibbs potential to be a function of the invariants of the conjugate stress tensor and then using the conditions resulting from the entropy inequality, (ii) using theory of generators and invariants and (iii) expanding Gibbs potential in the conjugate stress tensor using Taylor series about a known configuration and then using the conditions resulting from the entropy inequality. The constitutive theories resulting from these three approaches are compared for equivalence between them as well as their merits and shortcomings. The constitutive theory for the heat vector can also be derived either directly using the conditions resulting from the entropy inequality or using the theory of generators and invariants. The derivation of the constitutive theory for the heat vector using the theory of generators and invariants with the complete set of argument tensors yields a more comprehensive constitutive theory for the heat vector. In the work, we consider both approaches. Summaries of the constitutive theories using parallel approaches (as described above) resulting from the entropy inequality expressed in terms of Helmholtz free-energy density are also presented and compared for equivalence with the constitutive theories derived using Gibbs potential.

Development of Mathematical Models and Computational Framework for Multi-physics Interaction Processes

Abstract: This paper presents development of mathematical models for multi-physics interaction processes in which the physics of solids, liquids and gases are described using conservation laws, appropriate constitutive equations and equations of state in Eulerian description. The use of conservation laws in Eulerian description for all media of an interaction process and the choice of the same dependent variables in the resulting governing differential equations (GDEs) for solids, liquids and gases ensure that their interactions are intrinsic in the mathematic model. In the development of the constitutive equations and the equations of state, the same dependent variables are also utilized as those in the conservation laws. The dependent variables of choice due to the Eulerian description (which is necessary for liquids and gases) are density, pressure, velocities, temperature, heat fluxes and stress deviations. For solid, liquids and gases the development of constitutive equations is based on rate constitutive equa...

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.