正交加筋复合材料夹层板弯曲问题求解

正交加筋均质芯材基于一阶剪切变形理论,并采用δ函数描述其非连续性,复合材料面板采用Kirchhoff薄板假设,以面板面内位移和结构整体横向位移为响应函数,通过能量原理推导了正交加筋芯材复合材料夹层板的静力学平衡方程。考虑四边简支边界条件,采用双傅立叶级数位移函数求解了正交各向异性复合材料面板正交加筋均质芯材夹层板受均布载荷作用的弯曲响应,通过将夹层板的位移和应力响应与有限元计算结果进行对比,验证了文中求解方法的正确性。     

一种复合材料加筋夹芯板弯曲正应力工程计算方法

复合材料加筋夹芯板作为复合材料基本板架结构力学性能分析单元,是由夹芯板和加强筋组成,其蒙皮由不同厚度、不同材料和一定铺设角度的单层板叠合而成。利用材料力学理论和经典复合材料层合板理论,将蒙皮等效成正交各向异性层合板,推导一般情况下的复合材料加筋夹芯板中性轴位置控制方程,并采用等效截面方法,将加筋夹芯板截面等效成单一材料的组合截面,提出复合材料加筋夹芯板弯曲正应力的工程计算公式。复合材料加筋夹芯板各部分的最大弯曲正应力由模量比和距中性轴位置共同决定。本文提出的加筋夹芯板弯曲正应力工程计算方法,与有限元计算结果十分接近,主要弯曲正应力计算值与有限元值误差不超过10%,可以满足工程上的计算要求。此公式形式上和各向同性材料弯曲正应力的计算公式一致,给掌握复合材料板架结构应力水平带来方便。     

轮印载荷作用下波纹型夹层板格强度特性分析

针对轮印块状载荷下的波纹型夹层板格结构,建立了应力分析计算方法。该方法基于Mindlin-Reissner板理论的夹层板格整体弯曲计算和经典板理论的芯材间上面板的局部弯曲计算,并将二者叠加得到轮印载荷下夹层板格总的弯曲特性。开发了基于MATLAB的计算程序,能方便地调整夹层板格尺寸及轮印块载荷的位置、尺寸和载荷值,计算相应的板格变形和各特征点应力值。讨论了结构尺寸参数、轮印载荷尺寸参数等对上面板局部弯曲应力及板格整体弯曲应力的影响特性,为这类结构的设计和优化提供有益的参考。     

芯层可压缩的夹层梁动态刚度矩阵研究

该文推导了考虑芯层垂向压缩变形影响的夹层梁的动态刚度矩阵,为动态刚度矩阵方法提供了一种新的单元类型。首先给出了一种考虑夹层梁芯层垂向压缩变形影响的夹层梁位移模式,推导了相应的夹层梁动能和势能,根据Hamilton原理推导了其控制微分方程,按动态刚度矩阵的一般推导过程推导了考虑芯层垂向压缩变形影响的夹层梁动态刚度矩阵。计算结果表明文中推导的夹层梁动态刚度矩阵是正确可靠的;在夹层梁的动态刚度矩阵推导和高频振动计算中考虑芯层垂向压缩变形是合理的。     

含坑点腐蚀的壳体有限元方法

建立了坑点腐蚀壳板的分层模型(腐蚀层+完好层),求出了腐蚀层的等效材料常数(等效弹性模量和等效泊松比).开展了坑点腐蚀的应力集中分析,坑点腐蚀壳板的应力集中可分为薄膜应力集中和弯曲应力集中.以超参数壳元为基础推导了坑点腐蚀壳体单元,导出了坑点腐蚀壳体单元的刚度矩阵和等效结点载荷向量的有限元表达格式,单元刚度矩阵通过沿壳体厚度方向的分段积分求得,在积分时腐蚀层的材料常数取力学等效的材料常数,在计算单元等效结点载荷向量时考虑了由腐蚀引起的偏心载荷,在求解单元应力时考虑了坑点腐蚀应力集中的影响,并对应力进行了相应修正.     

含坑点腐蚀的壳体有限元方法

建立了坑点腐蚀壳板的分层模型(腐蚀层+完好层),求出了腐蚀层的等效材料常数(等效弹性模量和等效泊松比)。开展了坑点腐蚀的应力集中分析,坑点腐蚀壳板的应力集中可分为薄膜应力集中和弯曲应力集中。以超参数壳元为基础推导了坑点腐蚀壳体单元,导出了坑点腐蚀壳体单元的刚度矩阵和等效结点载荷向量的有限元表达格式,单元刚度矩阵通过沿壳体厚度方向的分段积分求得,在积分时腐蚀层的材料常数取力学等效的材料常数,在计算单元等效结点载荷向量时考虑了由腐蚀引起的偏心载荷,在求解单元应力时考虑了坑点腐蚀应力集中的影响,并对应力进行了相应修正。     

波纹夹层板固有频率的一阶Zig-Zag理论计算方法

在波纹夹层板微振动时,认为面板不仅承受弯曲作用,还承受剪切作用;心层承受剪切作用,同时仅承受波纹母线方向的弯曲作用。在夹层板的上下面板和心层分别应用一阶Zig-Zag理论,根据波纹心层的具体形状,列出夹层板的几何方程。通过Hamilton原理,建立夹层板的微振动微分方程。根据边界条件,用双傅里叶级数的方法求解方程,确定特征值,求得夹层板的振动频率。经过算例验证,该方法计算的前8阶固有频率与有限元法或其他文献结果相吻合。     

游艇泡沫夹层结构有限元分析方法

以一艘泡沫夹层玻璃钢材质双体游艇的帽形骨材结构为研究对象,考虑有芯和无芯两种情况,分别施加相同的边界条件和载荷,强度有限元计算结果表明,有无泡沫芯材两种模型的等效应力、最大剪应力以及最大变形的结果及应力变形分布情况等几乎相同,分析夹层板结构芯材直接计算方法,认为不能用简单的一层板单元代替泡沫芯材夹层板。     

方形蜂窝夹芯夹层板弯曲问题的新解法

文章针对方形夹芯夹层板弯曲问题提出了一种新的解法。所提方法未采用传统的芯层均匀等效做法,而直接对其离散的模型进行分析,考虑芯层的离散特性,将离散芯层和上下面板结合起来,运用能量原理建立方形蜂窝夹芯夹层板统一的弯曲控制方程。假设夹层板位移为双傅立叶级数形式,采用伽辽金法求解。对固支和简支矩形方形蜂窝夹芯夹层板数值仿真结果表明,文中方法得到的结果与有限元数值解吻合良好。该方法为有效、快捷地分析夹层板的力学性能提供了新的方法和途径。     

浮力材料和橡胶格栅夹层板振动响应试验对比研究

[目的]为探究芯材对格栅夹层板振动的影响规律,[方法]以格栅夹层板为研究对象,通过试验对比浮力材料格栅夹层板和橡胶格栅夹层板在不同状态下的振动响应差异,重点分析芯材对两型板抑振效果的影响。[结果]结果表明,空气中浮力材料格栅夹层板在中低频段(0～1 000 Hz)内的振动响应较低,橡胶格栅夹层板在高频段(1 000～3 000 Hz)内的振动响应较低;水中由于附加质量及附加阻尼效应的影响,夹层板体质量和芯材阻尼因素对板振动响应的影响程度被弱化,夹层结构的整体及板格局部弯曲刚度成为主导性影响因素,浮力材料格栅夹层板在全频段(0～3 000 Hz)内的振动响应均低于橡胶格栅夹层板的。[结论]为降低振动响应,格栅夹层板芯材的刚度应接近格栅的刚度;此外,芯材密度越小,阻尼越低,格栅夹层板在空气中和水中的振动响应差异就越大。     

基于等效截面的复合材料板格弯曲正应力计算方法

复合材料板格作为复合材料基本板架结构力学性能的最小分析单元,是由不同厚度、不同材料和不同铺设角度的单层板叠合而成。利用材料力学理论和经典复合材料层合板理论,推导一般情况下的复合材料板格中性轴位置控制方程,并采用等效截面方法,提出复合材料板格各单层弯曲正应力的计算公式。复合材料板格各单层的最大正应力由模量比和距中性轴位置共同决定。此公式形式上和各向同性材料弯曲正应力的计算公式一致,从而将弯曲正应力计算公式由各向同性材料扩展到各向异性材料,为掌握复合材料板架结构应力水平提供方便。此公式形式简洁,便于工程应用。     

Optimisation of laser-welded sandwich panels with multiple design constraints

This paper investigates the possibilities for structural optimisation of laser-welded sandwich panels with an adhesively bonded core and uni-directional vertical webs. Closed form expressions for the equivalent stiffness and elastic buckling strength of laser-welded sandwich panels are discussed and numerically evaluated to demonstrate the effect of parameter variations on stress and deflection. Due to the number of design variables and constraints a structural optimisation method based on the method of moving asymptotes (MMA) is implemented and used to minimise the structural weight per square meter of panel for a typical accommodation deck configuration. It is concluded that, within the span of production parameters and rule requirements, substantial improvements can be made with or without an adhesively bonded core. Without core material and without any changes to the surrounding structure the structural weight for standard production panels can be reduced considerably, by reducing the face plate thickness and by using thinner and fewer webs. Additional weight can be saved by removing all but a few webs and injecting low-cost polyurethane foam into the cavities, giving added thermal–acoustic insulation, or by incorporating a more structural core with greater thickness and higher density, by which the free span of the sandwich panel can be increased.     

单向加筋板低频振动的简化建模精度影响因素

针对典型单向加筋板结构的低频振动问题,基于薄板弯曲理论,得到等效正交异性板计算公式,通过与有限元计算结果比较验证计算公式的正确性。分析质量等效、弯曲刚度等效与结构参数对简化方法精度的影响规律,并通过附加弯曲刚度比对筋条截面高度、筋条数量和基板厚度等3项结构参数进行定量比较分析,对简化方法的适用范围产生量化认识,为加筋板简化建模的应用场景提供参考性建议。     

考虑横向剪切的双层板架临界载荷计算

本文考虑横向剪切效应,建立了一种计算双层板架结构临界载荷的方法：将复杂的双层板架结构从其相邻结构中分离出来,用弹性约束计及相邻结构的影响,用正交异性板的方法描述其力学特性,用能量法求解双层板架结构临界载荷。结果表明该方法可靠,尤其适合在工程方案的论证阶段应用。     

Load-bearing characteristics of marine complex sandwich composites considering unequal elastic modulus in tension and compression

The panel and core materials of sandwich composite usually have the characteristics of unequal elastic modulus in tension and compression. However, in the numerical calculation of sandwich composite, it is usually considered as the material with the same tensile modulus or compression modulus, which often leads to larger calculation errors. The test results show that when the elastic modulus of tension and compression is about 10 times different, the maximum calculated stress and maximum deflection will be more than twice different. In view of the complexity of sandwich composite structure, based on the bi-modulus model of laminated plates, a simplified theoretical formula and numerical calculation method are proposed for bi-modulus sandwich composite structures in this paper. Furthermore, the accuracy of the proposed numerical calculation method of bi-module is verified by the experimental study of composite single-layer plate structure and sandwich composite cabin structure. The results show that the error between the improved numerical calculation method and the experimental measurement results is basically within 6%. Meanwhile, the numerical method based on field variables has wide application range and high convergence, and can be used to calculate complex marine composite structures.     

船体曲率板感应加热成形工艺研究

[目的]在船舶建造过程中,板材的弯曲成形工艺不仅影响建造成本及周期,而且其成形精度也会影响船舶的水动力性能及其运营成本。[方法]针对船体板材双曲率成形效率低且精度差等问题,首先以感应加热作为热源,实现热弯成形,得到典型的帆形曲率板;然后通过高效的热?弹?塑性有限元(TEP FE)计算及基于弯曲力矩的弹性有限元计算,再现板材双曲率热弯成形的力学响应;同时,研究感应加热过程工艺参数影响板材弯曲成形的力学机理,提出线性逼近迭代二分法,实现板材热弯成形中加热位置和热源移动速度等工艺规划,并进行板材热弯成形过程及参数的有限元计算验证。[结果]结果显示,采用基于规划的工艺参数计算分析所得面外弯曲变形与目标曲率板的弯曲形状相当吻合。[结论]研究结果验证了线性逼近迭代二分法在实际工程应用中的可行性和准确性,并为曲率板成形工艺的优化提供了新的解决方案。     

复合材料螺旋桨弯扭耦合刚度特性分析

[目的]复合材料螺旋桨的弯扭耦合变形程度反映了桨叶的刚度特性,而桨叶刚度特性又与其水动力性能存在一定的相关性,将从刚度的角度对复合材料螺旋桨的纤维铺层进行优化设计.[方法]首先,以DTMB 4383复合材料螺旋桨为研究对象,基于复合材料螺旋桨流固耦合自迭代算法,构建桨叶弯扭刚度数值计算方法;然后,分别在桨叶铺设单向碳纤...     

钢夹层板数值模拟技术(英文)

Sandwich plate systems (SPS) are advanced materials that have begun to receive extensive attention in naval architecture and ocean engineering. At present, according to the rules of classification societies, a mixture of shell and solid elements are required to simulate an SPS. Based on the principle of stiffness decomposition, a new numerical simulation method for shell elements was proposed. In accordance with the principle of stiffness decomposition, the total stiffness can be decomposed into the bending stiffness and shear stiffness. Displacement and stress response related to bending stiffness was calculated with the laminated shell element. Displacement and stress response due to shear was calculated by use of a computational code write by FORTRAN language. Then the total displacement and stress response for the SPS was obtained by adding together these two parts of total displacement and stress. Finally, a rectangular SPS plate and a double-bottom structure were used for a simulation. The results show that the deflection simulated by the elements proposed in the paper is larger than the same simulated by solid elements and the analytical solution according to Hoff theory and approximate to the same simulated by the mixture of shell-solid elements, and the stress simulated by the elements proposed in the paper is approximate to the other simulating methods. So compared with calculations based on a mixture of shell and solid elements, the numerical simulation method given in the paper is more efficient and easier to do.     

Some analytical results for the initial phase of bottom slamming

The deformation of boat hull bottom panels during the initial phase of slamming is studied analytically using a linear elastic Euler–Bernoulli beam as a representation of the cross section of a bottom panel. The slamming pressure is modeled as a high-intensity peak followed by a lower constant pressure, traveling at constant speed along the beam. The problem is solved using a Fourier sine integral transformation in space and a Laplace–Carson integral transformation in time. Deflection and bending moment as functions of time and position for different speeds, bending stiffnesses, etc. are given. In particular the effect of slamming load traveling speed on structural response of the simplified bottom structure is investigated. It is found that rather large deflections and bending moments are encountered at certain speeds of the pressure, which suggests that bottom panels may benefit from tailoring their stiffness and mass properties such that loads are reduced. This would vary with boat particulars and operation (deadrise angle, mass, speed, sea state, etc). The importance of the high-intensity pressure peak often encountered during slamming is also studied. It is seen that for relatively slow moving slamming loads the pressure peak has little influence. However, for faster moving loads its influence can be significant.     

饱和冲量及其等效方法在舱室内爆炸中的应用

[目的]对于受到爆炸脉冲载荷冲击作用的船体结构,基于饱和冲量现象的相关研究表明,仅根据最大载荷幅值和脉冲总冲量来设计船体结构是不合理的,需探究工程应用中的饱和冲量现象。[方法]首先,总结饱和冲量概念的提出及研究发展;然后,以舱室内爆炸为典型算例,分析内爆炸载荷的曲线特性及结构响应特征;最后,基于饱和等效方法将复杂的内爆炸载荷等效为矩形脉冲载荷,采用理论及数值方法对等效载荷进行计算。[结果]结果表明:在舱室内爆炸准静态超压情况下普遍存在饱和冲量现象,实际工程应用中爆炸载荷会对结构造成较大的塑性变形,通常超过10倍板厚;而运用基于饱和冲量的等效方法分析,所得结果与数值仿真结果的误差小于10%。[结论]运用此方法可更准确地得出结构塑性动力响应结果,在结构抗冲击设计优化时,还可减少繁琐的复杂非线性数值计算,使设计更高效。