基于修正偶应力理论的几种微细观板梁模型

发布时间：2018-01-08 22:14

本文关键词：基于修正偶应力理论的几种微细观板梁模型　出处：《沈阳航空航天大学》2017年硕士论文　论文类型：学位论文

【摘要】：当构件的尺寸处于微/纳米量级时,试件尺寸越小其刚度和强度越大,这种现象被称为尺度效应。传统的连续介质理论因不包含任何内禀特征参数,无法解释这种现象;而偶应力理论引入了尺度参数,可以唯象的描述这种现象。因此,进一步分析微尺度材料的尺度效应无论从理论上还是从工程上都将具有十分重要的意义。本文基于修正的偶应力理论建立了若干仅包含一个材料内禀特征参数的微尺度板/梁模型,并对其力学响应的尺度效应进行了分析,具体工作可概括为:1.基于Yang等提出的各向同性修正偶应力理论建立了若干微尺度梁模型。首先,建立了适用于各种边界条件的微尺度轴向功能梯度梁的弯曲静力模型,并提出了一种模量折算策略,利用经典梁单元求解了微尺度轴向功能梯度梁的弯曲问题。其次,建立了微尺度Reddy变截面梁的自由振动模型。研究了变截面微梁自由振动问题的尺度效应,并讨论了横向剪切变形对自振频率计算的影响。2.基于Chen等提出的各向异性新修正偶应力理论建立了若干微尺度板模型。首先,建立了微尺度正交铺设Reddy层合板的自由振动模型,并通过算例讨论了尺度参数对四边简支层合板自振频率的影响,并对比了不同板理论计算结果的异同。其次,建立了适用于复杂边界条件的微尺度Reddy层合板自由振动有限元模型,并通过算例分析了铺设角、边界条件、宽厚比等对微尺度Reddy层合板自振频率的影响。然后,建立了微尺度角铺设层合板的弯曲静力模型。通过算例讨论了铺设角对弯曲变形尺度效应的影响。最后,建立了未经简化的微尺度层合板自由振动模型,并通过数值算例的对比讨论了常用的几个简化假设对微尺度四边简支层合板自振频率的影响以及适用范围。
[Abstract]:When the member size is in the order of micro / nanometer, the smaller the specimen size, the greater the stiffness and strength. This phenomenon is called scale effect. The traditional continuum theory does not contain any intrinsic characteristic parameters. This phenomenon cannot be explained; And the theory of couple stress introduces the scale parameter, which can describe this phenomenon phenomenologically. Further analysis of the scale effect of microscale materials will be of great significance both in theory and in engineering. In this paper, based on the modified even stress theory, we have established some materials containing only one intrinsic characteristic parameter. Microscale plate / beam model. The scale effect of the mechanical response is analyzed, and the concrete work can be summarized as: 1. Based on the isotropic modified couple stress theory proposed by Yang et al, some micro-scale beam models are established. The bending static model of micro-scale axial functionally gradient beams for various boundary conditions is established, and a modulus conversion strategy is proposed. The classical beam element is used to solve the bending problem of micro-scale axial functionally gradient beams. Secondly. The free vibration model of micro-scale Reddy beams with variable cross-section is established and the scale effect of the free vibration of micro-beams with variable cross-section is studied. The influence of transverse shear deformation on the calculation of natural vibration frequency is discussed. 2. Based on the anisotropic modified couple stress theory proposed by Chen et al, some microscale plate models are established. The free vibration model of Reddy laminates with micro-scale orthogonal laying is established, and the influence of scale parameters on the natural vibration frequency of simply supported laminated plates with four edges is discussed by an example. In addition, the finite element model of free vibration of micro-scale Reddy laminated plates suitable for complex boundary conditions is established, and the laying angle is analyzed by an example. The effect of boundary condition, width to thickness ratio on the natural vibration frequency of microscale Reddy laminates. The bending static model of micro-scale angular laminated plate is established. The influence of laying angle on the scale effect of bending deformation is discussed through an example. Finally, an unsimplified free vibration model of micro-scale laminated plate is established. The effect of several simplified hypotheses on the natural vibration frequency of micro-scale simply supported laminated plates with four edges and its application range are discussed by comparison of numerical examples.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB30

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