P. Mohan

Bio: P. Mohan is an academic researcher from Virginia Tech. The author has contributed to research in topics: Bending of plates & Finite element method. The author has an hindex of 5, co-authored 7 publications receiving 122 citations.

Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

Abstract: Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.

Updated Lagrangian Formulation of a Flat Triangular Element for Thin Laminated Shells

Abstract: An updated Lagrangian formulation of a three-node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells. The flat shell element is obtained by combining the discrete Kirchhoff theory plate bending element and a membrane element that is similar to the Allman element but a derivative of the linear strain triangular element. Results are presented for large-rotation static response analysis of a cantilever beam under end moment, cylindrical shell under pinching and stretching loads, a hemispherical shell under pinching and stretching loads, and a ring plate under a line load; for dynamic response analysis of a cylindrical panel; and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel. To estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures, static analysis of an apex-loaded circular arch is performed. The arch is a building block of a large inflatable structure. The results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software ABAQUS, demonstrating the accuracy of the present formulation. HE two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly. The curved shell elements can be computationally very expensive, especially in the case of nonlinear analysis, because of the complexity of the formulation and the need to compute the curvature information. Flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements. Though a large number of elements are required to accurately model curved structures, the analysis is computational ly less expensive because of extremely simple formulation. Updated Lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature. In an updated Lagrangian formulation, all of the variables are referred to a known configuration, the reference configuration, which is updated continuously during the deformation process. If the rigid-body modes are removed from the total or incremental displacements, the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used. In a linearized incremental formulation, the stresses are computed using linear strain-displacement relations. The tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix. The stiffness matrices resulting from the nonlinear terms in the strain-displacement relations are neglected, resulting in very economical analysis. If the rigid-body modes are not removed, all nonlinear terms in the strain-displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix. A three-node flat triangular shell element was introduced by Argyris et al.2 for nonlinear elastic stability problems. This formula

Control of Thermal Deformations of Spherical Mirror Segment

Abstract: Control of thermal deformations of a thin hexagonal spherical mirror segment using discrete and distributed actuators is presented. To determine the effectiveness of the actuators in controlling the thermal deformations of the mirror segment, a comparative study is conducted using two different models of the mirror‐ actuator system: 1) the mirror mounted on kinematic supports and controlled by piezoelectric strips bonded to the rear surface of themirrorand 2 )themirrormounted on force actuators, which are used to supportthemirroraswell as to control the surface deformations of the mirror. The performance of evenly distributed strips and that of strips placed at near-optimal locations obtained using heuristic integer programming are also compared. Both the force actuators and the piezoelectric strips are found to be equally effective in controlling the surface deformations of the mirror. A major drawback of the force actuators is the increase in the overall weight of the system, which is undesirable for space applications. On the other hand, the piezoelectric strips are very lightweight, and hence a large number of such strips can be used to control the surface distortions of the mirror, without imposing a weight penalty. The piezoelectric strips appear to be promising candidates for static shape control of e exible structures in space. Nomenclature b = side of graphite/epoxy plate, m d33 = piezoelectric strain constant, m/V E = root mean square error of the mirror surface distortions f j = control inputs (force applied to the force actuators or the voltage applied to the piezoelectric strips ) h = thickness of graphite/epoxy plate, m m = number of nodes of the e nite element model n = number of force actuators or piezoelectric strips u = correction to the transverse displacement W = middee ection of graphite/epoxy plate, m a ij = ine uence coefe cients w = deformed shape (transverse displacement) of the mirror

Geometrically nonlinear analysis of composite plates and shells using a flat triangular shell element

Abstract: An updated Lagrangian formulation of a three node flat triangular shell element is presented for geometrically non-linear analysis of laminated plates and shells. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element that is similar to the Allman element, but a derivative of the Linear Strain Triangular (LST) element. Results are presented for static response analysis (snap-back behavior of a cylindrical panel, large rotation response of a cantilever beam under an end moment, cylindrical shell under pinching and stretching loads and hemispherical shell under pinching and stretching loads); for dynamic response analysis of a cylindrical panel; and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel. The element will be used in the near future for the analysis of large inflatable structures which are highly flexible and are expected to undergo large deformations and rotations. In order to estimate the accuracy of the present formulation in predicting the nonlinear response of such large flexible structures, static analysis of an apex-loaded circular arch is performed. The arch presented is a building block of a large inflatable structure. The present results are in good agreement with the results available in the existing literature and those obtained using the commercial finite element software ABAQUS, demonstrating the accuracy of the present formulation.

Analysis of General Shells Under Deformation Dependent Pressure loads Using a Flat Triangular Shell Element

Abstract: 1. Abstract Finite element large deformation analysis of general shells under deformation dependent pressure loads using a three-noded flat triangular shell element is presented. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element similar to the Allman element, but derived from the Linear Strain Triangular (LST) element. The follower effects of the pressure load are included in the finite element formulation. The pressure stiffness matrix and the deformation dependent pressure load vector in a Cartesian coordinate system are systematically derived from the principle of virtual work. Results are presented for a cantilever beam under uniform external pressure and a thin circular ring under non-uniform external pressure. The element will be used in the near future for the analysis of a large inflatable structure which is highly flexible and is expected to undergo large deformations and rotations. In order to estimate the accuracy of the present formulation in predicting the nonlinear response of large structures, analysis of a thin circular arch under internal and external pressure loads is performed. The arch presented is a building block of a large inflatable structure. The present results are in good agreement with the results available in the existing literature and those obtained using the commercial finite element software ABAQUS, where ever applicable, demonstrating the accuracy of the present formulation.

Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells

Abstract: This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. Most of the theories and finite elements that have been proposed over the last thirty years are in fact based on these types of approaches. The paper has been divided into three parts. Part I, has been devoted to the description of possible approaches to plate and shell structures: 3D approaches, continuum based methods, axiomatic and asymptotic two-dimensional theories, classical and mixed formulations, equivalent single layer and layer wise variable descriptions are considered (the number of the unknown variables is considered to be independent of the number of the constitutive layers in the equivalent single layer case). Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformability, zig-zag effects and interlaminar continuity, have been discussed and summarized by the acronimC -Requirements. Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymtotic and continuum based approaches have been overviewed. Classical theories and their refinements are first considered. Both case of equivalent single-layer and layer-wise variables descriptions are discussed. The so-called zig-zag theories are then discussed. A complete and detailed overview has been conducted for this type of theory which relies on an approach that is entirely originated and devoted to layered constructions. Formulas and contributions related to the three possible zig-zag approaches, i.e. Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera ones have been presented and overviewed, taking into account the findings of a recent historical note provided by the author. Finite Element FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are first outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist of a specific application of finite element techniques, such as hybrid methods and so-called global/local techniques. The extension of finite elements that were originally developed for isotropic one layered structures to multilayerd plates and shells are first discussed. Works based on classical and refined theories as well as on equivalent single layer and layer-wise descriptions have been overviewed. Development of available zig-zag finite elements has been considered for the three cases of zig-zag theories. Finite elements based on other approches are also discussed. Among these, FEs based on asymtotic theories, degenerate continuum approaches, stress resultant methods, asymtotic methods, hierarchy-p,_-s global/local techniques as well as mixed and hybrid formulations have been overviewed.

Popular benchmark problems for geometric nonlinear analysis of shells

Abstract: In most, if not all, of the previous work on finite element formulation and nonlinear solution procedures, results of geometric nonlinear benchmark problems of shells are presented in the form of load-deflection curves. In this paper, eight sets of popularly employed benchmark problems are identified and their detailed reference solutions are obtained and tabulated. It is hoped that these solutions will form a convenient basis for subsequent comparison and that the tedious yet inaccurate task of reconstructing data points by graphical measurement of previously reported load-deflection curves can be avoided. Moreover, the relative convergent difficulty of the problems are revealed by the number of load increments and the total number of iterations required by an automatic load incrementation scheme for attaining the converged solutions under the maximum loads.

A survey of recent shell finite elements

Abstract: Since the mid-1960s when the forms of curved shell finite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The first two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell finite elements over the past 15 years. It is hoped that this will be a befitting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell finite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites. Copyright © 2000 John Wiley & Sons, Ltd.

A fluid-structure interaction model of insect flight with flexible wings

Abstract: We present a fluid-structure interactions (FSI) model of insect flapping flight with flexible wings. This FSI-based model is established by loosely coupling a finite element method (FEM)-based computational structural dynamic (CSD) model and a computational fluid dynamic (CFD)-based insect dynamic flight simulator. The CSD model is developed specifically for insect flapping flight, which is capable to model thin shell structures of insect flexible wings by taking into account the distribution and anisotropy in both wing morphology involving veins, membranes, fibers and density, and in wing material properties of Young's modulus and Poisson's ratios. The insect dynamic flight simulator that is based on a multi-block, overset grid, fortified Navier-Stokes solver is capable to integrate modeling of realistic wing-body morphology, realistic flapping-wing and body kinematics, and unsteady aerodynamics in flapping-wing flights. Validation of the FSI-based aerodynamics and structural dynamics in flexible wings is achieved through a set of benchmark tests and comparisons with measurements, which contain a heaving spanwise flexible wing, a heaving chordwise-flexible wing with a rigid teardrop element, and a realistic hawkmoth wing rotating in air. A FSI analysis of hawkmoth hovering with flapping flexible wings is then carried out and discussed with a specific focus on the in-flight deformation of the hawkmoth wings and hovering aerodynamic performances with the flexible and rigid wings. Our results demonstrate the feasibility of the present FSI model in accurately modeling and quantitatively evaluating flexible-wing aerodynamics of insect flapping flight in terms of the aerodynamic forces, the power consumption and the efficiency.