Edge Constraints Research Articles

Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

직사각형 후판의 면외 진동인텐시티 해석

A numerical method is presented for an out-of-plane structural intensity analysis of rectangular thick plates with arbitrary elastic edge constraints. The method adapts an assumed mode method based on Timoshenko beam functions to obtain the velocities and internal forces needed for a structural intensity analysis. To verify the presented method, the structural intensity of a square thick plate under harmonic force excitation, for which four edges are simply supported, is analyzed, and the result is compared with existing solutions using the assumed mode method based on trigonometric functions. In addition, numerical analyses are carried out for a rectangular-shaped thick plate under harmonic force excitations, of which three edges are simply supported and one edge utilizes an arbitrary elastic edge constraint. These numerical examples show the good accuracy and applicability of the presented method for rectangular thick plates with arbitrary edge constraints.

Selective Boosting Algorithm for Maximizing the Soft Margin

当前,boosting 集成学习算法研究主要集中于最大化弱学习器凸组合的间隔或软间隔,该凸组合几乎使用了生成的所有弱学习器,然而这些弱学习器间存在大量的相关性和冗余,增加了训练和分类过程的时空复杂度.针对这一问题,在LPBoost 基础上提出了一种选择性boosting 集成学习算法,称为SelectedBoost.在每次迭代生成新的弱学习器以后,通过计算新生成的弱学习器与已有弱学习器的相关度和差异度,并结合当前集成的强学习器的准确率来判断是否选择该弱学习器.另外,当前的一系列boosting 算法(如AdaBoost,LPBoost,ERLPBoost 等),本质上是基于已生成的1 个或者多个弱学习器来更新样本权重,但与弱学习器相比,强学习器更能代表当前的决策面.因此,SelectedBoost 通过在带约束的间隔最大化问题中引入更加严格的强学习器边界约束条件,使得该算法不仅参考弱学习器边界,同时还参考已生成的强学习器来更新样本权重,进而提高算法的收敛速度.最后,与其他有代表性的集成学习算法进行实验比较,结果表明,该方法在收敛率、分类准确性以及泛化能力等方面均具有比较明显的优势.;Research of traditional boosting algorithms mainly focuses on maximizing the hard or soft margin of the convex combination among weak hypotheses. The weak learners are often all used in the combination, even though some of them are more, or less related. This increases the time complexity of the hypotheses’ training and test. To ease the redundancies of the base hypotheses, this paper presents a selective boosting algorithm called SelectedBoost for classifying binary labeled samples, which is based on LPBoost. The main idea of the algorithm is to discard as many hypotheses as possible according to their relevance and diversity. Furthermore, this paper introduces an edge constraint for every strong hypothesis to speed up the convergence when maximizing the soft margin of the combination of the weak hypotheses. The experimental results show that this algorithm can achieve both better performance and less generalization error compared to some representative boosting algorithms.

Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration

A scrutiny of the literature reveals that the free vibration characteristics of stiffened composite hypar shell with cutout are missing. So a generalized finite element formulation for the stiffened hyperbolic paraboloidal shells bounded by straight edges (commonly called as hypar shells) is attempted using an eight-noded curved quadratic isoparametric element for shell with a three-noded beam element for stiffener. Numerical problems of earlier investigators are solved as benchmark problems to validate the approach. A number of problems are further solved by varying the size of the cutouts and their positions with respect to the shell centre for different edge constraints. The results are presented in the form of figures and tables. The results are further analysed to suggest guidelines to select optimum size and position of the cutout with respect to shell centre considering the different practical constraints.

C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates

The Refined Zigzag Theory (RZT) has been recently developed for the analysis of homogeneous, multilayer composite and sandwich plates. The theory has a number of practical and theoretical advantages over the widely used First-order Shear Deformation Theory (FSDT) and other types of higher-order and zigzag theories. Using FSDT as a baseline, RZT takes into account the stretching, bending, and transverse shear deformations. Unlike FSDT, this novel theory does not require shear correction factors to yield accurate results for a wide range of material systems including homogeneous, laminated composite, and sandwich laminates. The inplane zigzag kinematic assumptions, which compared to FSDT add two additional rotation-type kinematic variables, give rise to two types of transverse shear strain measures – the classical average shear strain (as in FSDT) and another one related to the cross-sectional distortions enabled by the zigzag kinematic terms. Consequently, with a fixed number of kinematic variables, the theory enables a highly accurate modeling of multilayer composite and sandwich plates even when the laminate stacking sequence exhibits a high degree of transverse heterogeneity. Unlike most zigzag formulations, this theory is not affected by such theoretical anomalies as the vanishing of transverse shear stresses and forces along clamped boundaries.In this paper, six- and three-node, C0-continuous, RZT-based triangular plate finite elements are developed; they provide the best compromise between computational efficiency and accuracy. The element shape functions are based on anisoparametric (aka interdependent) interpolations that ensure proper element behavior even when very thin plates are modeled. Continuous edge constraints are imposed on the transverse shear strain measures to derive coupled-field deflection shape functions, resulting in a simple and efficient three-node element. The elements are implemented in ABAQUS – a widely used commercial finite element code – by way of a user-element subroutine.The predictive capabilities of the new elements are assessed on several elasto-static problems, which include simply supported and cantilevered laminated composite and sandwich plates. The numerical results demonstrate that the new RZT-based elements provide superior predictions for modeling a wide range of laminates including highly heterogeneous sandwich laminations. They also offer substantial improvements over the existing plate elements based on FSDT as well as other higher-order and zigzag-type elements.

Buckling and Vibration of Elastically Restrained Standing Vertical Plates

This paper investigates the buckling and vibration of heavy standing plates with rotational elastic edge constraints. The discrete singular convolution (DSC) method as a powerful numerical technique is applied to derive the governing eigenvalue equation. Convergence and comparison studies are conducted to authenticate the correctness and accuracy of the DSC approach. Accurate first-known vibration solutions for elastically restrained vertical plates subjecting to body forces/self-weight are presented. Some contour mode shapes for the vibration of elastically restrained vertical plates are also depicted for illustration.

A lower bound on the Chvátal-rank of Antiwebs

In [Holm, E., L. M. Torres and A. K. Wagler, On the Chvátal-rank of linear relaxations of the stable set polytope, International Transactions in Operational Research 17 (2010), pp. 827–849; Holm, E., L. M. Torres and A. K. Wagler, On the Chvátal-rank of Antiwebs, Electronic Notes in Discrete Mathematics 36 (2010), pp. 183–190] we study the Chvátal-rank of the edge constraint and the clique constraint stable set polytopes related to antiwebs. We present schemes for obtaining both upper and lower bounds. Moreover, we provide an algorithm to compute the exact values of the Chvátal-rank for all antiwebs with up to 5,000 nodes. Here we prove a lower bound as a closed formula and discuss some cases when this bound is tight.

Network Coding in Node-Constrained Line and Star Networks

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.

Free vibration analysis of moderately thick antisymmetric cross-ply laminated rectangular plates with elastic edge constraints

This study presents a simple formulation for studying the free vibration of shear-deformable antisymmetric cross-ply laminated rectangular plates having translational as well as rotational edge constraints. The aim is to fill the void in the available literature with respect to the free vibration results of antisymmetric cross- ply laminated rectangular plates. The spatial discretization of the resulting mathematical model in five field variables is carried out using the two-dimensional Differential Quadrature Method (DQM). Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Effects of stiffness parameters, geometrical features, moduli ratio and lamination schemes on the natural frequencies are studied.

Effect of inplane edge constraints on natural frequencies of simply supported doubly curved shallow shells

Reasonably accurate natural frequencies are presented for simply supported shallow shells on rectangular planform subjected to 55 possible combinations of edge constraints. Thin shallow shell theory is used. Accurate natural frequencies of doubly curved shallow shells are presented and can be used for benchmarking by researchers as well as reference data for practicing engineers. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.

Free Vibration of Laminated Composite Hypar Shell Roofs with Cutouts

Use of laminated composites in civil engineering structural components including shell roofs is increasing day by day due to their light weight, high specific strength, and stiffness properties. In the present paper, laminated composite hypar shell (hyperbolic paraboloidal shells bounded by straight edges) roofs with cutouts are analyzed for their free vibration characteristics using finite element method. An eight‐noded curved shell element is used for modeling the shell. Specific numerical problems of earlier investigators are solved to compare their results with the present formulation. A number of problems are further solved where the size of the cutouts and their positions with respect to the shell centre are varied for different edge constraints. The results are furnished in the form of figures and tables. The results are examined thoroughly to arrive at some meaningful conclusions useful to designers.

On the Chvátal rank of linear relaxations of the stable set polytope

AbstractWe study the Chvátal rank of two linear relaxations of the stable set polytope, the edge constraint and the clique constraint stable set polytope. For some classes of graphs whose stable set polytope is given by 0/1‐valued constraints only, we present either the exact value of the Chvátal rank or upper bounds (of the order of their largest cliques and stable sets), which improve the bounds previously known from the literature (of the order of the graph itself).

On the Chvátal-rank of Antiwebs

Abstract We present an algorithm for computing both upper and lower bounds on the Chvatal-rank of antiwebs, starting from the edge constraint stable set polytope. With the help of this algorithm we have been able to compute the exact values of the Chvatal-rank for all antiwebs containing up to 5,000 nodes. Moreover, the algorithm can be easily adapted to start from the clique constraint stable set polytope.

Study on the vibration characteristics of a finite-width corrugated cylindrical shell piezoelectric transducer

Coupled extensional and flexural vibrations of an ultrasonic piezoelectric transducer are studied in the paper. The ultrasonic piezoelectric transducer is made of piezoelectric polymer PVDF films and modeled as a corrugated cylindrical shell with a finite width in the ridge direction, which consists of multiple pieces of circular cylindrical surfaces smoothly connected along their ridges. The classical shell theory is used to obtain the theoretical solution. Effects of the edge constraints on vibrational characteristics of the resonant frequencies, mode shapes, and internal forces are investigated for a corrugated ultrasonic piezoelectric transducer consisting of a few circular pieces each with a thickness of about 40 microm, radius of 5 mm, and span angle of 120 degrees.

Strongly chordal and chordal bipartite graphs are sandwich monotone

A graph class is sandwich monotone if, for every pair of its graphs G 1=(V,E 1) and G 2=(V,E 2) with E 1?E 2, there is an ordering e 1,?,e k of the edges in E 2?E 1 such that G=(V,E 1?{e 1,?,e i }) belongs to the class for every i between 1 and k. In this paper we show that strongly chordal graphs and chordal bipartite graphs are sandwich monotone, answering an open question by Bakonyi and Bono (Czechoslov. Math. J. 46:577---583, 1997). So far, very few classes have been proved to be sandwich monotone, and the most famous of these are chordal graphs. Sandwich monotonicity of a graph class implies that minimal completions of arbitrary graphs into that class can be recognized and computed in polynomial time. For minimal completions into strongly chordal or chordal bipartite graphs no polynomial-time algorithm has been known. With our results such algorithms follow for both classes. In addition, from our results it follows that all strongly chordal graphs and all chordal bipartite graphs with edge constraints can be listed efficiently.

On listing, sampling, and counting the chordal graphs with edge constraints

We discuss the problems to list, sample, and count the chordal graphs with edge constraints. The objects we look at are chordal graphs sandwiched by a given pair of graphs where we assume that at least one of the input graphs is chordal. The setting is a natural generalization of chordal completions and deletions. For the listing problem, we give an efficient algorithm running in polynomial time per output with polynomial space. As for the sampling problem, we give two clues that indicate that a random sampling is not easy. The first clue is that we show #P-completeness results for counting problems. The second clue is that we give an instance for which a natural Markov chain suffers from an exponential mixing time. These results provide a unified viewpoint from algorithms’ theory to problems arising from various areas such as statistics, data mining, and numerical computation.

The influence of particle shape, volume fraction and distribution on post-necking deformation and fracture in uniaxial tension of AA5754 sheet materials

Finite element analysis was performed over a small particle field, edge constraint plane strain post-necking model. The aim is to understand the roles of particle shape, volume fraction and distribution over the post-necking deformation and fracture of AA5754-O sheet materials. For models containing one single particle, the post-necking deformation decreases when the particle varies from circular to elliptical. The inter-particle spacing, the major parameter of distribution to determine whether a pair of particles belongs to a stringer or not, was varied for models with two particles of circular or elliptical shape. The general trend is that the post-necking deformation and fracture strains decrease with decreasing spacing between particles. There is considerable difference in terms of both fracture topographies and strains for models containing 16 particles when distributions varied from random/uniform to stringer distributions. The post-necking deformation and fracture strains monotonically decrease with particle volume fractions for models with 4–64 particles of random or stringer distribution. This indicates that the post-necking behavior for AA5754-O alloys where the matrix material is rather ductile is not solely controlled by a single or pair of particles although they may become initiation places of damage. Multiple damaging sources such as stringers or large particles can act cooperatively and speed up the damaging propagation of the material, and therefore produce small post-necking deformation and early fracture. The center clustering of particles can be beneficial for post-necking behavior and bendability of sheet materials.

Spectral quadrangulation with orientation and alignment control

This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the Morse-Smale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigen-problem we can generate a scalar field on the mesh whose Morse-Smale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the Morse-Smale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.

Sensitivity of the response of thick cross-ply doubly curved panels to edge clamping

A heretofore unavailable analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick doubly-curved panel of rectangular plan-form, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach, is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the C3-type clamped boundary condition prescribed at all four edges. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a cross-ply spherical panel. The primary focus of the present study is to investigate the effect of edge clamping on the response of a thick laminated doubly-curved panel, while keeping the surface-parallel edge constraints unaltered. Important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, material property, thickness and curvature effects, and edge clamping as well as their interactions.