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.

Delamination in cross-ply laminated beams using the layerwise theory

Abstract: A finite element model based on the layerwise theory of Reddy is developed for the analysis of delamination in the [90/0]S cross-ply laminated beams. The Heaviside step function was adopted in the formulation to express the discontinuous interlaminar displacement fields of delaminated layers. Also, to accommodate the moderately large rotations of the beam, the von Karman type nonlinear strain field is used in the formulation. The finite element model is verified by comparing the present solutions with those available in the literature. It is shown that the present finite element model is able to capture accurate local stress fields and the strain energy release rates. Then the model is used to study delaminated cross-ply laminates under bending loads. The influence of boundary conditions and number of layers on the strain energy release rates is studied. Also, the growth of delamination is investigated for a pure bending case, and the mode of delamination growth is identified. The influence of geometric nonlinearity on the delamination growth is also investigated as the delamination advances. It is found that geometric nonlinearity does not significantly alter the delamination kinematics and strain energy release rates.

Principles of Continuum Mechanics: A Study of Conservation Principles with Applications

Abstract: As most modern technologies are no longer discipline-specific but involve multidisciplinary approaches, undergraduate engineering students should be introduced to the principles of mechanics so that they have a strong background in the basic principles common to all disciplines and are able to work at the interface of science and engineering disciplines. This textbook is designed for a first course on principles of mechanics and provides an introduction to the basic concepts of stress and strain and conservation principles. It prepares engineer-scientists for advanced courses in traditional as well as emerging fields such as biotechnology, nanotechnology, energy systems, and computational mechanics. This simple book presents the subjects of mechanics of materials, fluid mechanics, and heat transfer in a unified form using the conservation principles of mechanics.

Necessity of law of balance/equilibrium of moment of moments in non-classical continuum theories for fluent continua

Abstract: In the non-classical theories for fluent continua, the presence of internal rotation rates and their gradients arising due to the velocity gradient tensor necessitate existence of moment tensor. The Cauchy moment tensor acting on the faces of the deformed tetrahedron (derived using Cauchy principle) and the gradients of the rates of total rotations are a rate of work conjugate pair in addition to the rate of work conjugate Cauchy stress tensor and rate of strain tensor. It is well established that in such non-classical continuum theories the Cauchy stress tensor is non-symmetric and the antisymmetric components of the Cauchy stress tensor are balanced by the gradients of the Cauchy moment tensor, balance of angular momenta balance law. In the non-classical continuum theories incorporating internal rotation rates and conjugate Cauchy moment tensor that are absent in classical continuum theories, the fundamental question is “are the conservation and balance laws used in classical continuum mechanics sufficient to ensure dynamic equilibrium of the deforming volume of matter?" If one only considers conservation and balance laws used in classical continuum theories, then the Cauchy moment tensor is non-symmetric. Thus, requiring constitutive theories for the symmetric as well as non-symmetric Cauchy moment tensors. The work presented in this paper shows that when the thermodynamically consistent constitutive theories are used for the symmetric as well as antisymmetric Cauchy moment tensors, non-physical and spurious solutions result even in simple flows. This suggests that perhaps the additional conjugate tensors resulting due to the presence of internal rotation rates, namely the Cauchy moment tensor and the antisymmetric part of Cauchy stress tensor, must obey some additional law or restriction so that the spurious behavior is precluded. The paper demonstrates that in the non-classical theory with internal rotation rates considered here the balance of moment of moments balance law and the equilibrium of moment of moments are in fact identical. When this balance law is considered, the Cauchy moment tensor becomes symmetric, hence eliminating the constitutive theory for the antisymmetric Cauchy moment tensor and thereby eliminating spurious and non-physical solutions. The necessity of this balance/equilibrium law is established theoretically, its derivation is presented using rate considerations, and its necessity is also demonstrated by a model problem using thermoviscous incompressible fluid as an example. The findings reported in this paper hold for all fluent continua, compressible as well as incompressible.

Modeling the dynamics of filaments for medical applications

Abstract: We present a theoretical formulation based on the Cosserat theory of rods to describe the motion of rod-like filaments (e.g., surgical threads) used in surgical suturing. The equations of motion are simplified using certain approximations and the resulting equations are solved using the finite difference (centered difference) scheme in time and space. The boundary conditions involve the specification of the force and moment at the free end of the thread and symmetry conditions commonly encountered during surgeries. Numerical simulations of suture threads with genuine material parameters and geometries specific to surgical scenarios are presented.

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.