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.

J-Integral for Mode I Linear Elastic Fracture Mechanics in h, p, k Mathematical and Computational Framework

Abstract: This paper presents an infrastructure for computations, and computations of J-integral for mode I linear elastic fracture mechanics in h, p, k mathematical and computational framework using finite element formulations based on the Galerkin method with weak form and least squares processes. Since the differential operators in this case are self-adjoint, both Galerkin method with weak form and least square processes yield unconditionally stable computational processes. h, p, k framework permits higher order global differentiability approximations in the finite element processes, which are necessitated by physics, calculus of continuous and differentiable functions, and higher order global differentiability features of the theoretical solutions. The investigations considered in this paper are summarized here: (i) J-integral expression is derived and it is shown that its path independence requires the governing differential equations (GDEs) to be satisfied in the pointwise sense in the numerical process, (ii)...

Theories and analyses of functionally graded circular plates

Abstract: This paper presents the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded axisymmetric circular plates. The classical, first-order, and third-order shear deformation theories are presented, accounting for through-thickness variation of two-constituent functionally graded material, modified couple stress effect, and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.

Riemann shock tube: 1D normal shocks in air, simulations and experiments

Abstract: This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space–time finite element processes based on minimization of the space–time residual functional. The space–time local approximation functions for space–time p-version hierarchical finite elements are considered in higher order Hk,p(Ω‾xte) spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space–time strip corresponding to a time increment Δt and then time march to obtain the e...

Pattern Transformation Induced Waisted Post-Buckling of Perforated Cylindrical Shells

Abstract: • Waisted post-buckling pattern transformation is concluded for clamped cellular cylindrical shells. • Shell theory can be used to analyze negative Poisson's ratio formed by waisted post-buckling. • Load-carrying capacities of cellular cylindrical shells undergo sudden drop but recover subsequently. • Waisted post-buckling behavior could appear for thin-walled shell without external support. • Waisted post-buckling patterns may be found on other curved structures such as cylindrical panels. A comprehensive investigation on the extremely large post-buckling deformation of perforated cylindrical shells is conducted using experiments and verified with an analytical shell model and nonlinear finite element simulations. A “waisted” post-buckling configuration, which is characterized by uniform shrinking in the middle section of the perforated cylindrical shell, is identified. The waisted behavior is attributed to the triggering of a pattern transformation under compressive load that shows special hyperelastic metamaterial characteristics. The load-carrying capacity of waisted post-buckling suffers a sudden drop and then recovers when the holes are completely collapsed and closed. Plenty of design parameters can be utilized to enrich variations of the waisted post-buckling responses. The negative Poisson's ratio induced by pattern transformation plays a key role in forming the waisted post-buckling modes. This special hyperelastic metamaterial behavior can be easily achieved by fixing the boundaries and adjusting the geometric parameters of the shell. By comparing the characteristics of a porous cylindrical shell with those appeared for an equivalent porous panel, it is highlighted that pattern transformation can occur in a thinner porous cylindrical shell without lateral support. The waisted post-buckling modes of a perforated cylindrical shell are stable, and the shell is invulnerable to the progressively increasing applied loads. In comparison, an ordinary cylindrical shell may snap from one mode to another in the post-buckling process. Moreover, we find that some non-closed cylindrical panels can also buckle into the waisted-like modes. These findings can be applied to the construction of functional devices for soft robotics, actuators, and structural protection for facilities, etc.

On multigrid methods for the solution of least-squares finite element models for viscous flows

Abstract: There is a vast literature on least-squares finite element models (LSFEM) applied to fluid dynamics problems. The hp version of the least-squares models is computationally expensive, which necessitates the usage of elegant methods for solving resulting systems of equations. Amongst some of the schemes used for solving large systems of equations is the element-by-element (EBE) solution technique, which has found widespread use in least-squares applications. However, the use of EBE techniques with Jacobi preconditioning leads to very little performance gains as compared to solving a non-preconditioned system. Because of such considerations, the hp version LSFEM solutions are computationally intensive. In this study, we propose to solve the LSFEM systems using the multigrid method, which offers superior convergence rates compared to the EBE–JCG. We demonstrate the superior convergence of the Multigrid solver compared to Jacobi preconditioning for the wall-driven cavity and backward facing step problems using...

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.