Rakesh K. Kapania

Bio: Rakesh K. Kapania is an academic researcher from Virginia Tech. The author has contributed to research in topics: Finite element method & Aeroelasticity. The author has an hindex of 14, co-authored 44 publications receiving 466 citations.

Static and Vibration Analyses of General Wing Structures Using Equivalent-Plate Models

Abstract: An efficient method, using equivalent plate model, is developed for studying the static and vibration analyses of general built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory, the so-called First-order Shear Deformation Theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. This is in contrast to previous equivalent plate model methods which have used simple polynomials, known to be prone to numerical ill-conditioning, as the trial functions. The present developments are evaluated by comparing the results with those obtained using MSC/NASTRAN, for a set of examples. These examples are: (i) free-vibration analysis of a clamped trapezoidal plate with (a) uniform thickness, and (b) non-uniform thickness varying as an airfoil, (ii) free-vibration and static analyses (including skin stress distribution) of a general built-up wing, and (iii) free-vibration and static analyses of a swept-back box wing. The results obtained by the present equivalent plate model are in good agreement with those obtained by the finite element method.

Vibration of Plate with Curvilinear Stiffeners Using Mesh-Free Method

Abstract: The element-free Galerkin method, which is based on the moving-least-squares approximation, is developed for vibration analysis of unitized structures (e.g., a plate with curvilinear stiffeners). The plate and stiffeners are modeled using the first-order shear deformation theory and Timoshenko beam theory, respectively. The moving-least-squares approximation does not satisfy the delta function property. Consequently, an approximation method (e.g., the well-known penalty method) must be used for imposing essential boundary conditions. A key benefit of using element-free Galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes. Numerical results for different stiffeners, configurations, and boundary conditions are presented. All results are verified using the commercial finite-element software ANSYS. Excellent agreement is seen in all cases. A comparison of the present formulations with other available results for stiffened plates is also made. The mesh-free approach yields highly accurate results for the plates with curvilinear stiffeners.

Structural and Aeroelastic Characteristics of Truss-Braced Wings: A Parametric Study

Abstract: flexible in nature. This paper presents a set of parametric studies of truss-braced-wing configurations to understand the influence of the wing geometry parameters on the wing structural and aeroelastic characteristics. The primary parametersconsideredherearethewinghalf-span,strutsweep,spanwiselocationofwing-strutjoint,andnumberof truss members in the wing configuration. Each truss-braced-wing parametric configuration is sized based on strength considerations and studied for aeroelastic behavior. The results indicate strong influence of all the parameters considered here. For most cases, increasing the half-span monotonically increases the wing weight and reduces both the natural frequencies and the flutter speed. A larger difference between the wing- and strut sweep angles is seen to increase wing weight, but with a positive influence on flutter speed for various truss-braced-wing configurations. The spanwise intersection location has distinct optima for wing weight and flutter speed, which typically lie in between 55 and 70%. These results are expected to provide guidance for future multidisciplinary design optimization studies for truss-braced-wing configurations.

Truss Topology Optimization with Simultaneous Analysis and Design

Abstract: Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by simultaneous analysis and design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.

Dynamic buckling of imperfection-sensitive shell structures

Abstract: Structural buckling under dynamic loads may occur at load levels that are less than the corresponding static loads. Presence of local geometric imperfections may induce an early buckling for both static and dynamic loadings. The phenomenon of "dynamic weakening" is studied for a general class of shell structures under a general class of time-dependent loadings. A doubly curved quadrilateral Love-Kirchhoff shell finite element is used. Geometric deviations of the shell middle surface are included within the element formulation by suitably modifying the strain-displacement relations. This is accomplished by retaining additional terms that are quadratic in spatial derivatives of imperfections and displacement components. The nonlinear equations of motion are written in the Lagrangian system and are solved by using an incremental algorithm based on Newmark's generalized operator. The dynamic responses up to buckling are obtained for a perfect spherical cap and an imperfect spherical cap both under external pressure, as well as a complete imperfect sphere under external pressure. Numerical results include the effects of amplitude of imperfection and thickness of shell on the dynamic buckling loads. The formulation is general and can be applied to obtain the dynamic buckling responses of a wide variety of shell structures.

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Generalized shape optimization without homogenization

Abstract: Two types of solutions may be considered in generalized shape optimization. Absolute minimum weight solutions, which are rather unpractical, consist of solid, empty and porous regions. In more practical solutions of shape optimization, porous regions are suppressed and only solid and empty regions remain. This note discusses this second class of problems and shows that a solid, isotropic microstructure with an adjustable penalty for intermediate densities is efficient in generating optimal topologies.

A critical review of established methods of structural topology optimization

Abstract: The aim of this article is to evaluate and compare established numerical methods of structural topology optimization that have reached the stage of application in industrial software. It is hoped that our text will spark off a fruitful and constructive debate on this important topic.

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.

Sensitivity of complex, internally coupled systems

Abstract: A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.