1. "Refined Plate Theory and Its Variants"
Shimpi, R. P.; AIAA Journal,
Vol. 40, No. 1, January 2002, pp 137146 
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. "Zerothorder Shear Deformation Theory for Plates"
Shimpi, R. P.;
AIAA Journal, Vol. 37, No. 4, April 1999, pp 524526 
Abstract:
The development of a simple and easytouse zerothorder 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 thinplate problems,
the finite elements based on the ZSDT will be free from shear locking.

3. "A New Layerwise Trigonometric Shear Deformation Theory
for Twolayered Crossply Beams"
Shimpi, R.P. and Ghugal, Y.M.;
Composites Science and Technology, Vol. 61, No. 9, July 2001, pp 12711283

Abstract:
A new layerwise trigonometric shear deformation theory for the analysis
of twolayered crossply laminated beams is presented. The number of primary
variables in this theory is even less than that of firstorder 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 shearstressfree
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 twolayered
crossply 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 153162 
Abstract:
A simple onedimensional 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 inplane displacement such that shearstress free
boundary conditions on the top and bottom surfaces of the beam element are
satisfied and the shearstress distribution is realistic in nature. Constitutive
relations between shearstresses and shearstrains are satisfied in all
the layers, and, therefore, shear correction factor is not required. Compatibility
at the layer interface in respect of inplane 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 shearstresses 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 Crossply Laminated Beams"
Shimpi, R.P. and Ghugal, Y.M.;
Journal of Reinforced Plastics and Composites, Vol. 18, No. 16, 1999, pp
15161543 
Abstract:
A Layerwise Trigonometric Shear Deformation Theory (LTSDT) for the analysis
of two layered crossply 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 stressfree
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 crossply 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 24432462 
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 2124 
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 crossply 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
255272 
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 Algorithmbased
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 2023 1998, Long Beach, CA, USA, AIAA981912, pp 17411751 (Publisher:
AIAA, Reston, VA, USA, 1998) 
Abstract:
This paper presents an approach for combining approximation models with
genetic algorithmbased 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 steadystate
behavior of simple GAs. Guidelines based on trustregion 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%. 