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1. "Refined Plate Theory and Its Variants"
Shimpi, R. P.; AIAA Journal,
Vol. 40, No. 1, January 2002, pp 137-146
Abstract: The development of a new refined plate theory and its two simple variants is given. The theories have strong commonality with the equations of classical plate theory (CPT). However, unlike CPT, these theories assume that lateral and axial displacements have bending and shear components such that bending components do not contribute toward shear forces and, likewise, shearing components doe not contribute toward bending moments. The theory and one of its variants are variationally consistent, whereas the second variants is variationally inconsistent and uses the relationships between moments, shear forces, and loading. It should be noted that, unlike any other refined plate theory, the governing equations as well as the expressions for moments and shear forces associated with this variant are identifical to those associated with the CPT, save for the appearance of a subscript. The effectiveness of the theory and its variants is demonstrated through an example. Surprisingly, the answers obtained by both the variants of the theory, one of which is variationally consistent and the other one is inconsistent, are same. The numerical example studied, therefore, not only brings out the effectiveness of the theories presented, but also, albeit unintentionally, supports the doubts, first raised by Levinson, about the so called superiority of variationally consistent methods.
2. "Zeroth-order Shear Deformation Theory for Plates"
Shimpi, R. P.;
AIAA Journal, Vol. 37, No. 4, April 1999, pp 524-526
Abstract: The development of a simple and easy-to-use zeroth-order shear deformation theory (ZSDT) for plates is discussed. The resulting ZSDT approach uses the lateral displacement itself, hence is more physically meaningful than Librescu's approach. With ZSDT, only physically meaningful entities are used. In the context of a finite element solution of thin-plate problems, the finite elements based on the ZSDT will be free from shear locking.
3. "A New Layerwise Trigonometric Shear Deformation Theory for Two-layered Cross-ply Beams"
Shimpi, R.P. and Ghugal, Y.M.;
Composites Science and Technology, Vol. 61, No. 9, July 2001, pp 1271-1283
Abstract: A new layerwise trigonometric shear deformation theory for the analysis of two-layered cross-ply laminated beams is presented. The number of primary variables in this theory is even less than that of first-order shear deformation theory, and moreover, it obviates the need for a shear correction factor. The sinusoidal function in terms of thickness coordinate is used in the displacement field to account for shear deformation. The novel feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relationships, satisfying the shear-stress-free boundary conditions at top and bottom of the beam and satisfying continuity of shear stress at the interface. The principle of virtual work is used to obtain the governing equations and boundary conditions of the theory. The effectiveness of the theory is demonstrated by applying it to a two-layered cross-ply laminated beam.
4. "A Beam Finite Element Based on Layerwise Trigonometric Shear Deformation Theory"
Shimpi, R.P. and Ainapure, A.V.;
Composite Structures, Vol. 53, No. 2, August 2001, pp 153-162
Abstract: A simple one-dimensional beam finite element, based on layerwise trigonometric shear deformation theory, is presented. The element has two nodes and only three degrees of freedom per node. Yet, it incorporates through the thickness sinusoidal variation of in-plane displacement such that shear-stress free boundary conditions on the top and bottom surfaces of the beam element are satisfied and the shear-stress distribution is realistic in nature. Constitutive relations between shear-stresses and shear-strains are satisfied in all the layers, and, therefore, shear correction factor is not required. Compatibility at the layer interface in respect of in-plane displacement is also satisfied. It is to be noted that the element developed is free from shear locking. The results obtained are accurate and show good convergence. Unlike many other elements, transverse shear-stresses are evaluated directly using constitutive relations. The efficacy of the present element is demonstrated through the examples of static flexure and free vibration.
5. "Layerwise Trigonometric Shear Deformation Theory for Two Layered Cross-ply Laminated Beams"
Shimpi, R.P. and Ghugal, Y.M.;
Journal of Reinforced Plastics and Composites, Vol. 18, No. 16, 1999, pp 1516-1543
Abstract: A Layerwise Trigonometric Shear Deformation Theory (LTSDT) for the analysis of two layered cross-ply laminated beams, taking into account discrete layer transverse shear deformation effects, is presented. The theory is as simple as the first order shear deformation theory and does not require shear correction factor. The sinusoidal function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The most important feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the stress-free boundary conditions at top and bottom of the beam and satisfying continuity at the interface. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. The system of governing differential equations is reduced to a single sixth order linear differential equation. A two layered asymmetric cross-ply laminated beam is considered for the numerical study to validate the accuracy of the theory.
6. "On the Theory of Discrete Structural Model Analysis and Design"
Panditta, I.K., Shimpi, R.P. and Prasad, K.S.R.K.;
International Journal of Solids and Structures, Vol. 36, No. 16, June 1999, pp 2443-2462
Abstract: Exclusive theory for analysis of Structural Models (comprising of springs, masses, dash pots, etc.) is presented by adapting the electrical network theory. It commences a brief statement of a new Principle of Quasi Work (PQW), relevant to this theory. Derivations presented here include theorems addressing maximum displacements, relative flexibilities, sensitivity analysis of global flexibilities, inverse problem of load prediction and interpolation of stiffnesses and flexibilities of the Structural Models. Finally a `Design Equation' capable of providing a starting point which more or less satisfies all the displacement constraints for iterative design employing a pair of estimated starting points for design iterations (within or outside feasible region) is evolved. Simple substantive illustrations are included to demonstrate the potential of these theoretical developments.
7. "A Zigzag Model for Laminated Composite Beams"
Arya, H., Shimpi, R.P. and Naik, N.K.;
Composite Structures, Vol. 56, No. 1, April 2002, pp 21-24
Abstract: In the present work, a zigzag model for symmetric laminated beam is developed. This model uses a sine term to represent the nonlinear displacement field across the thickness as compared to a third order polynomial term in conventional theories. Transverse shear stress and strain are represented by a cosine term as compared to parabolic term. This model satisfies displacement and transverse shear stress continuity at the interface. Zero transverse shear stress boundary condition at the top and bottom of the beam are also satisfied. The numerical results indicates that the present model predicts very accurate results for displacement and stresses for symmetric cross-ply laminated beam, even for small length to thickness ratio. The results are also compared with a simplified theory of same class.
8. "A Review of Refined Shear Deformation Theories for Isotropic and Anisotropic Laminated Beams"
Ghugal, Y.M. and Shimpi, R.P.;
Journal of Reinforced Plastics and Composites, Vol. 20, No. 3, 2001, pp 255-272
Abstract: A review of displacement and stress based refined theories for isotropic and anisotropic laminated beams is presented. Various equivalent single layer and layerwise theories for laminated beams are discussed together with their merits and demerits. Exact elasticity solutions for the beam problems are cited, wherever available. Various critical issues, related with beam theories, based on the literature reviewed are presented.
9. "Combining Approximation Concepts with Genetic Algorithm-based Structural Optimization Procedures"
Nair, P.B., Keane, A.J. and Shimpi, R.P.;
Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Vol. 2, 1998, Proceedings of the 1998 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit and AIAA/ASME/AHS Adaptive Structures Forum. Part 2 (of 4), Apr 20-23 1998, Long Beach, CA, USA, AIAA-98-1912, pp 1741-1751 (Publisher: AIAA, Reston, VA, USA, 1998)
Abstract: This paper presents an approach for combining approximation models with genetic algorithm-based design optimization procedures. An important objective here is to develop an approach which empirically ensures that the GA converges asymptotically to the optima of the original problem using a limited number of exact analysis. It is shown that this problem may be posed as a dynamic optimization problem, wherein the fitness function changes over successive generations. Criteria for selecting the design points where exact analysis should be carried out are proposed based on observations on the steady-state behavior of simple GAs. Guidelines based on trust-region methods are presented for controlling the generation delay before the approximation model is updated. An adaptive selection operator is developed to efficiently navigate through such changing and uncertain fitness landscapes. Results are presented for the optimal design problem of a 10 bar truss structure. It is shown that, using the present approach, the number of exact analysis required to reach the optima of the original problem can be reduced by more than 97%.