77,269 research outputs found
Optimal design of sandwich plates with honeycomb core
This work deals with the problem of the optimum design of a sandwich structure composed of two laminated skins and a honeycomb core. The goal is to propose a numerical optimisation procedure that does not make any simplifying hypothesis in order to obtain a true global optimal solution for the considered problem. In order to face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy. At the first level, we determine the optimum geometry of the unit cell together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. We will illustrate the application of our strategy to the least-weight design of a sandwich plate submitted to several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins
Optimal Uncertainty Quantification
We propose a rigorous framework for Uncertainty Quantification (UQ) in which
the UQ objectives and the assumptions/information set are brought to the
forefront. This framework, which we call \emph{Optimal Uncertainty
Quantification} (OUQ), is based on the observation that, given a set of
assumptions and information about the problem, there exist optimal bounds on
uncertainties: these are obtained as values of well-defined optimization
problems corresponding to extremizing probabilities of failure, or of
deviations, subject to the constraints imposed by the scenarios compatible with
the assumptions and information. In particular, this framework does not
implicitly impose inappropriate assumptions, nor does it repudiate relevant
information. Although OUQ optimization problems are extremely large, we show
that under general conditions they have finite-dimensional reductions. As an
application, we develop \emph{Optimal Concentration Inequalities} (OCI) of
Hoeffding and McDiarmid type. Surprisingly, these results show that
uncertainties in input parameters, which propagate to output uncertainties in
the classical sensitivity analysis paradigm, may fail to do so if the transfer
functions (or probability distributions) are imperfectly known. We show how,
for hierarchical structures, this phenomenon may lead to the non-propagation of
uncertainties or information across scales. In addition, a general algorithmic
framework is developed for OUQ and is tested on the Caltech surrogate model for
hypervelocity impact and on the seismic safety assessment of truss structures,
suggesting the feasibility of the framework for important complex systems. The
introduction of this paper provides both an overview of the paper and a
self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository
Research Papers). See SIAM Review for higher quality figure
A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields
A new noded polygonal plate element is proposed for the analysis of
plate structures comprising of thin and thick members. The formulation is based
on the discrete Kirchhoff Mindlin theory. On each side of the polygonal
element, discrete shear constraints are considered to relate the kinematical
and the independent shear strains. The proposed element: (a) has proper rank;
(b) passes patch test for both thin and thick plates; (c) is free from shear
locking and (d) yields optimal convergence rates in norm and
semi-norm. The accuracy and the convergence properties are demonstrated
with a few benchmark examples
A volume-averaged nodal projection method for the Reissner-Mindlin plate model
We introduce a novel meshfree Galerkin method for the solution of
Reissner-Mindlin plate problems that is written in terms of the primitive
variables only (i.e., rotations and transverse displacement) and is devoid of
shear-locking. The proposed approach uses linear maximum-entropy approximations
and is built variationally on a two-field potential energy functional wherein
the shear strain, written in terms of the primitive variables, is computed via
a volume-averaged nodal projection operator that is constructed from the
Kirchhoff constraint of the three-field mixed weak form. The stability of the
method is rendered by adding bubble-like enrichment to the rotation degrees of
freedom. Some benchmark problems are presented to demonstrate the accuracy and
performance of the proposed method for a wide range of plate thicknesses
The Optimal Uncertainty Algorithm in the Mystic Framework
We have recently proposed a rigorous framework for Uncertainty Quantification
(UQ) in which UQ objectives and assumption/information set are brought into the
forefront, providing a framework for the communication and comparison of UQ
results. In particular, this framework does not implicitly impose inappropriate
assumptions nor does it repudiate relevant information. This framework, which
we call Optimal Uncertainty Quantification (OUQ), is based on the observation
that given a set of assumptions and information, there exist bounds on
uncertainties obtained as values of optimization problems and that these bounds
are optimal. It provides a uniform environment for the optimal solution of the
problems of validation, certification, experimental design, reduced order
modeling, prediction, extrapolation, all under aleatoric and epistemic
uncertainties. OUQ optimization problems are extremely large, and even though
under general conditions they have finite-dimensional reductions, they must
often be solved numerically. This general algorithmic framework for OUQ has
been implemented in the mystic optimization framework. We describe this
implementation, and demonstrate its use in the context of the Caltech surrogate
model for hypervelocity impact
An integrated approach to the optimum design of actively controlled composite wings
The importance of interactions among the various disciplines in airplane wing design has been recognized for quite some time. With the introduction of high gain, high authority control systems and the design of thin, flexible, lightweight composite wings, the integrated treatment of control systems, flight mechanics and dynamic aeroelasticity became a necessity. A research program is underway now aimed at extending structural synthesis concepts and methods to the integrated synthesis of lifting surfaces, spanning the disciplines of structures, aerodynamics and control for both analysis and design. Mathematical modeling techniques are carefully selected to be accurate enough for preliminary design purposes of the complicated, built-up lifting surfaces of real aircraft with their multiple design criteria and tight constraints. The presentation opens with some observations on the multidisciplinary nature of wing design. A brief review of some available state of the art practical wing optimization programs and a brief review of current research effort in the field serve to illuminate the motivation and support the direction taken in our research. The goals of this research effort are presented, followed by a description of the analysis and behavior sensitivity techniques used. The presentation concludes with a status report and some forecast of upcoming progress
- …