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.

A non-classical third-order shear deformation plate model based on a modified couple stress theory

Abstract: A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.

Variable Kinematic Modelling of Laminated Composite Plates

Abstract: A displacement-based variable kinematic global–local finite element model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. The displacement field hierarchy contains both a conventional plate expansion (2-D) and a full layerwise (3-D) expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. The VKFE is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm. These models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free-edge effects).

Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators

Abstract: In the present work, a nonlinear thermo-electro-mechanical response of functionally graded piezoelectric material (FGPM) actuators is investigated. The theoretical formulation is based on the Timoshenko beam theory with the von Karman nonlinearity (in the form of midplane stretching), and a microstructural length scale is incorporated by means of the modified couple stress theory. A power-law distribution of thermal, electrical, and mechanical properties through beam thickness (or height) is assumed. The governing equations are derived using the principle of virtual displacements. A displacement finite element model of the theory is developed, and the resulting system of nonlinear algebraic equations is solved with the help of Newton's iteration method. Numerical results are presented for transverse deflection as a function of load parameters and out-of-plane boundary conditions. The parametric effects of microstructural length scale parameter, power-law index of the material distribution across the thickness, boundary conditions, beam geometry, and applied actuator voltage on the beam response are investigated through various numerical examples. The results reveal the existence of bifurcation (or critical states) for certain types of in-plane loads. For other load types, including out-of-plane loads, the beam undergoes a unique and stable deflection path that does not contain any critical point.

Thermal stresses and deflections of cross-ply laminated plates using refined plate theories

Abstract: Exact analytical solutions of refined plate theories are developed to study the thermal stresses and deflections of cross-ply rectangular plates. The state-space approach in conjunction with the Levy method is used to solve exactly the governing equations of the theories under various boundary conditions. Numerical results of the higher-order theory of Reddy for thermal stresses and deflections are compared with those obtained using the classical and first-order plate theories.

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.