Best theory diagram for metallic and laminated composite plates

ABSTRACT

Best theory diagrams (BTDs) are reported in this article for the static analysis of metallic and laminated composite plates. A BTD is a curve that provides the minimum number of unknown variables of a structural theory for a fixed error. The error is related to a given variable with respect to an exact or quasi-exact solution. The theories that belong to the BTD have been obtained by means of the axiomatic/asymptotic technique, and a genetic algorithm has been employed to obtain the BTD. The Carrera Unified Formulation (CUF) has been employed to obtain refined models, since the CUF can generate automatically, and in a unified manner, any type of plate model. Equivalent single layer (ESL) and layer-wise (LW) kinematics are discussed. Closed-form, Navier-type solutions have been employed, and attention has therefore been restricted to simply-supported plates. The influence of various geometries, material properties, and layouts has been considered, and their influence on the BTD has been evaluated. Furthermore, some known theories have been evaluated and compared with the BTD curve. The results suggest that the BTD and the CUF can be considered as tools to evaluate the accuracy of any structural theory against a reference solution in a systematic manner.     

Optimal lay-up design of variable stiffness laminated composite plates by a layer-wise optimization technique

The optimal lay-up design for the maximum fundamental frequency of variable stiffness laminated composite plates is investigated using a layer-wise optimization technique. The design variables are two fibre orientation angles per ply. Thin plate theory is used in conjunction with a p-element to calculate the fundamental frequencies of symmetrically and antisymmetrically laminated composite plates. Comparisons with existing optimal solutions for constant stiffness symmetrically laminated composite plates show excellent agreement. It is observed that the maximum fundamental frequency can be increased considerably using variable stiffness design as compared to constant stiffness design. In addition, optimal lay-ups for the maximum fundamental frequency of variable stiffness symmetrically and antisymmetrically laminated composite plates with different aspect ratios and various combinations of free, simply supported and clamped edge conditions are presented. These should prove a useful benchmark for optimal lay-ups of variable stiffness laminated composite plates.     

基于模糊进化规划和分层方法的神经网络设计方法

本文提出一种模糊进化规划，用于前向神经网络的设计．该方法通过对神经元的部分解群体的进化，缩短了个体的编码长度，显著地减轻了计算量，同时这种方法不但能够在很大程度上简化适应值的计算，更重要的是能够降低适应值空间的复杂性，从而能够加速进化算法收敛到全局最优点．仿真结果显示，本文提出的算法能够有效抑制进化规划算法初期收敛的发生，有效地提高多层前向神经网络收敛精度，并可获得更为简洁的网络结构．     

基于高分辨率类激活映射算法的弱监督目标实时检测

受益于深度学习的发展,目标检测技术在各类视觉任务中得到广泛关注。然而,获取目标的边框标注需要高昂的时间和人工成本,阻碍了目标检测技术在实际场景中的应用。为此,该文在仅使用图像类别标签的基础上,提出一种基于高分辨率类激活映射算法的弱监督目标实时检测方法,降低网络对目标实例标注的依赖。该方法将目标检测细划分为弱监督目标定位和目标实时检测两个子任务。在弱监督定位任务中,该文利用对比层级相关性传播理论设计了一种新颖的高分辨率类激活映射算法(HR-CAM),用于获取高质量目标类激活图,生成目标伪检测标注框。在实时检测任务中,该文选取单镜头多盒检测器(SSD)作为目标检测网络,并基于类激活图设计目标感知损失函数(OA-Loss),与目标伪检测标注框共同监督SSD网络的训练过程,提高网络对目标的检测性能。实验结果表明,该文方法在CUB200和TJAB52数据集上实现了对目标准确高效的检测,验证了该文方法的有效性和优越性。     

A variable kinematic shell formulation applied to thermal stress of laminated structures

In this article, the thermoelastic static analysis of multilayered shell structure is performed using some advanced theories, obtained by expanding the unknown displacement variables along the thickness direction using equivalent-single-layer (ESL) models, layer-wise (LW) models, and variable-kinematic models. The variable-kinematic models permit to reduce the computational cost of the analyses grouping some layers of the multilayered structure with ESL models and keeping the LW models in other zones of the multilayer. This model is here extended for the static analysis of uncoupled thermomechanical problems. The results obtained with the classical assumed linear temperature profile along the thickness of the shell are compared with those achieved with the calculated temperature profile solving the Fourier heat conduction equation. The used refined models are grouped in the Carrera’s unified formulation (CUF), and they accurately describe the displacement field and the stress distributions along the thickness of the multilayered shell. The shell element has nine nodes, and the mixed interpolation of tensorial components method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement, and the finite element method is used to solve them. Cross-ply plates and shells with simply supported edges, subjected to bisinusoidal thermal load are analyzed. Various aspect ratios and radius to thickness ratios are considered. The results, obtained with different theories within CUF context, are compared with the elasticity solutions given in the literature. From the results, it is possible to conclude that the shell element based on the CUF is very e?cient in the study of thermomechanical problems of composite structures. The variable-kinematic models combining the ESL with the LW models permit to have a reduction of the computational costs, with respect with the full LW models, preserving the accuracy of the results in localized layers.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Axiomatic/asymptotic analysis of refined layer-wise theories for composite and sandwich plates

This article deals with layer-wise (LW) models for composite and sandwich plates. Refined layer-wise models are built according to the Carrera Unified Formulation (CUF), which has been developed over the last decade for beams, plate, and shell theories. CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. In this article, displacement variables are expanded along the layer thickness through Legendre polynomials. Comparisons with previous analysis based on equivalent single layer (ESL) approaches are given. The effect of each term of the expansion on the accuracy of stress/displacement components for the static response of composite and sandwich plates is analyzed. Ineffective terms are discarded from the expansion in order to save computational cost. The reduced models obtained, which are denoted as mixed axiomatic/asymptotic models, are as accurate as full expansion models. Numerical analysis is restricted to closed-form solutions via Navier-type solutions. A number of problems related to laminated and sandwich structures are solved and related reduced models are built by varying geometrical, lay-up, and mechanical parameters. Results show that in some cases (in particular those related to sandwich plates) reduced layer-wise models can save up to 50% of the degrees-of-freedom of the full models without significant accuracy losses. It is found that the significant terms related to reduced models are very much subordinated to the problems considered and that from that point of view the use of a framework that can generate any theory, such as CUF, appears very suitable to build reduced models for plates.     

A variable ESL/LW kinematic plate formulation for free-vibration thermoelastic analysis of laminated structures

In this article, a fully-coupled thermoelastic formulation is developed to deal with the free-vibration analysis of multilayered plate composite and sandwich structure. Some advanced theories are obtained by expanding the unknown displacement variables along the thickness direction and using equivalent-single-layer (ESL) models, layer-wise (LW) models, and variable-kinematic models. The variable-kinematic models permit to reduce the computational cost of the analyses grouping some layers of the multilayered structure with ESL models and keeping the LW models in other zones of the multilayer. This model is here extended for the free-vibration analysis of fully-coupled thermomechanical problems. The used refined models are grouped in the Carrera unified formulation (CUF), and they accurately describe the displacement field and the temperature distributions along the thickness of the multilayered plate. The governing equations are derived from the principle of virtual displacement, and the finite element method (FEM) is employed to solve them. Isotropic plates, cross-ply composite plates, and sandwich structures with composite skins and simply-supported edges are analyzed. Various aspect ratios are considered. The results, obtained with different theories within CUF context, are compared with the elasticity solutions, and other higher-order analytical and FEM solutions given in the literature. From the results, it is possible to conclude that the plate element based on the CUF is very efficient in the study of thermomechanical problems of composite structures. The variable-kinematic models combining the ESL with the LW models, permit to have a reduction of the computational costs, respect with the full LW models, preserving the accuracy of the results.     

基于e–p曲线的软土地基非线性沉降的实用计算方法

软土地基侧向变形引起的沉降不可忽略。目前中国地基规范对软土地基的沉降主要是采用侧限压缩试验曲线进行一维压缩沉降计算,然后对该计算结果乘以一个经验修正系数来反映软土侧向变形等所产生的沉降,经验系数为1.1~1.7,变化大,缺乏量化取用方法。因此,侧向变形引起的沉降尚缺乏有效可靠的实用计算方法。基于e–p曲线和Duncan-Chang本构模型的概念提出了用e–p曲线求取软土的非线性切线模量Et的方法,然后把地基的沉降分解为有侧限的压缩沉降和侧向变形产生的沉降两部分。有侧限的压缩沉降采用传统的e–p曲线分层总和法计算,侧向变形的沉降用非线性切线模量Et进行分层总和法求得。模型简单、参数易获得,由此而建立了一个较简便实用的软土地基非线性沉降计算方法。并通过一个工程案例与实测结果、规范方法计算结果和有限元数值分析结果进行比较,说明方法的可行性。     

考虑覆盖层对地基应力分散效应的地基沉降计算方法探讨

对于软土地基上的建筑物的沉降计算,我国规范推荐采用分层总和法。分层总和法中地基附加应力的计算以点荷载作用下的半无限空间的Boussinesq解为基础。对于具有不同刚度和强度相差较大的地层而言,以此方法为基础计算得到的最终沉降往往偏大。本文提出一种基于多层弹性理论的考虑覆盖层对地基应力分散作用的地基沉降计算方法。这种方法的计算结果使地基中的应力水平较基于Boussinesq解的结果大幅降低,对于某工程实例而言,计算得到的地基中的总有效应力小于前期固结压力,土层的变形相对较小。工程实测的结果表明,所提出方法计算结果与实测结果较为接近。