基于稳定理论的剪切薄膜褶皱发展过程及其动力特性研究
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摘要
随着薄膜结构在建筑结构领域和航天器方面的大量应用,褶皱问题所带来的不利影响逐渐引起了人们的广泛关注。褶皱的出现不仅会影响到结构的表面精度,而且会改变结构的应力分布状况,影响结构的振动特性,并对风荷载作用下的气动特性产生不利影响。因此,必须对褶皱的形成特点和发展过程进行深入研究,从而掌握褶皱发展机理,及褶皱对薄膜力学性能的影响规律,以有助于对褶皱现象进行有效控制。虽然实际工程中薄膜结构的几何形状复杂多变,而平面张拉薄膜是一种形式最简单的薄膜结构,但通过对平面张拉薄膜的研究可以忽略次要因素,深入分析从薄膜结构中抽象出来的共性问题,揭示出在褶皱产生和发展过程中,结构力学性能的变化规律。因此,本文将以平面薄膜为研究对象,分析褶皱的产生和发展规律,以及对结构静力特性和动力性能的影响。
本文在薄膜结构褶皱问题方面的研究工作,可以分为计算理论与数值分析两个方面：
(1)计算理论方面：基于稳定理论,提出了考虑沿褶皱方向张拉应力的影响时,临界压应力的计算方法,并得到了波长和幅值等构形参数的表达式。通过与已有文献的试验结果和数值分析结果的比较,表明所得计算公式是合理有效的,并具有良好的精度。
(2)数值分析方面的研究工作,主要分为以下几个部分：
a.提出并验证了将褶皱的产生和发展过程进行三阶段划分的思想。通过对褶皱产生和发展过程的研究发现：褶皱首先发生在压应力最早出现的部位,然后向中间部位扩展,最后达到稳定。因此,该过程表现为：初始阶段、扩展阶段和稳定阶段三个典型阶段,并对每一阶段的褶皱特点进行研究。通过对褶皱产生和发展过程的研究,可以认识褶皱机理,掌握褶皱对薄膜结构力学特性的影响规律。同时通过这种划分,能够有效地衡量褶皱发展程度,并方便地对处于特定状态的褶皱性状进行研究和描述。
b.提出并验证了褶皱控制临界值的思想,为防止结构因面外变形和褶皱数量的迅速增大(多)而失效提供量化依据。对剪切矩形薄膜进行仿真试验研究发现,当薄膜的面外位移达到膜材厚度的1%时,就必须对褶皱进行控制,否则结构的面外变形会迅速增大,而导致结构失效。
c.以薄膜厚度、张拉预应力、初始缺陷为关键参数,对其在褶皱产生和发展过程中的影响进行了研究。结果表明：随着薄膜厚度的增加,褶皱数量减少,幅值和波长变大,但面外位移与厚度的比值减小,因此厚度越小,褶皱对结构的不利影响越大；增大张拉预应力,可以延迟褶皱的出现,增强结构的面外稳定性,但是材料的强度安全储备会减少,因此应合理控制张拉预应力;初始缺陷主要影响到褶皱的位置,尤其是褶皱最先出现的位置,而对褶皱数量、波长、幅值等的影响不明显。
d.对褶皱发展不同阶段的结构动力特性进行了研究。结果表明：频率随剪切位移角的变化,也表现出三个典型阶段：初始阶段(频率下降),扩展阶段(频率波动上升)和稳定阶段(频率缓慢下降)。在稳定阶段,由于结构会发生二次屈曲,频率可能出现小幅波动。振型的变化与频率相比较为复杂,但总体趋势表现为与褶皱方向一致的振型增多。
With a large number of membrane structures used in the fields of building structures and spacecrafts, negative effects of wrinkles have aroused wide concern. The existences of wrinkles not only affect the surface accuracy of a structure, but also change its stress distributions and vibration performance and further affect the aerodynamic characteristics under wind load. Therefore, it is required that further researches be performed on the formation characteristics and the transition of wrinkles. Practical membranes are more complex and diverse in geometry than planar ones, and planar tension membrane is just one of the simplest structures, analysis on a simple planar membrane will contribute a lot to the attention on the common problems abstracted from membrane structures by excluding secondary factors and reveal the variation of mechanical properties following transition of wrinkles. Therefore, in this paper a planar membrane is mainly concerned to study the wrinkles and their influences on structures.
The content of this paper can be divided into two aspects of theory and numerical calculation:
(1) One part is on the theoretical analysis. Based on the stability theory, a new method of calculating critical compressive stress was proposed, in which the effect of tension stress along the wrinkling direction is considered. Afterwards, the formulas of wavelength and amplitude were easily obtained. Comparisons with the experiment results and the numerical results in the literatures show that the formulas given in this paper are valid, and have good accuracy.
(2) The other part is on the numerical analyses as the following:
a. A new method which divided the transition of the membrane wrinkles into three states was proposed. Generation and development of wrinkles were studied. The results show that:wrinkles appear first in the positions where compressive stress occurs earliest, and then expand to the middle part gradually until they are stable. The whole wrinkling process can be characterized by three typical stages:The Initial-Stage, The Expansion-Stage and The Stable-Stage. And the characteristics of each stage were studied. Through this part of study, the mechanism of wrinkles can be cognized. And the influence laws of mechanical properties affected by wrinkles can be mastered. And also, through this division, the degree of transition can be effectively measured; the wrinkles characters in a particular state can easily be studied and described.
b. Proposes and confirms a critical value to control wrinkles, in order to provide the quantitative basis to prevent the structural failure caused by the deformation and the wrinkles increases. The simulation researches on the shear rectangular tensile membrane show that:Wrinkles should be restricted to such an extent that the ratio between the out-plane displacement and the membrane thickness is less than1%. Otherwise, the out-plane deformation would increase rapidly, and cause the structure's failure.
c. The influence of thickness, initial prestress and initial imperfections on the wrinkles are studied. The results show that:with the increase of thickness, wrinkles decrease in number, but increase in wavelength and amplitude. However, the ratio of out-plane displacement to thickness decreases. Therefore, the smaller the thickness is, the larger the wrinkling impact is. Increase of the prestress can enhance the structure's out-plane stability and delay the appearance of wrinkles, but decrease the safety margin of structures. Therefore, the tension prestress should also be confined to a reasonable range. The initial imperfections mainly affect the location of wrinkles, especially the location where wrinkles appears first. But their influence on the wrinkling number, wavelength and amplitude is not obvious.
d. Dynamic characteristics of the structure at the different wrinkling stages are studied. The results show that:The frequency variation with shear displacement angle can also be characterized by three stages:The Initial-Stage in which the frequency is declining, The Expansion-Stage in which the frequency is raising fluctuates, and The Stable-Stage in which the frequency is declining again. In The Stable-Stage, because of the second-buckling of the membrane structure, the frequency appears to fluctuate. The change of the mode shape is much more complex than that of frequency. The mode shapes tend to increase along the wrinkles.
本文在薄膜结构褶皱问题方面的研究工作,可以分为计算理论与数值分析两个方面：
(1)计算理论方面：基于稳定理论,提出了考虑沿褶皱方向张拉应力的影响时,临界压应力的计算方法,并得到了波长和幅值等构形参数的表达式。通过与已有文献的试验结果和数值分析结果的比较,表明所得计算公式是合理有效的,并具有良好的精度。
(2)数值分析方面的研究工作,主要分为以下几个部分：
a.提出并验证了将褶皱的产生和发展过程进行三阶段划分的思想。通过对褶皱产生和发展过程的研究发现：褶皱首先发生在压应力最早出现的部位,然后向中间部位扩展,最后达到稳定。因此,该过程表现为：初始阶段、扩展阶段和稳定阶段三个典型阶段,并对每一阶段的褶皱特点进行研究。通过对褶皱产生和发展过程的研究,可以认识褶皱机理,掌握褶皱对薄膜结构力学特性的影响规律。同时通过这种划分,能够有效地衡量褶皱发展程度,并方便地对处于特定状态的褶皱性状进行研究和描述。
b.提出并验证了褶皱控制临界值的思想,为防止结构因面外变形和褶皱数量的迅速增大(多)而失效提供量化依据。对剪切矩形薄膜进行仿真试验研究发现,当薄膜的面外位移达到膜材厚度的1%时,就必须对褶皱进行控制,否则结构的面外变形会迅速增大,而导致结构失效。
c.以薄膜厚度、张拉预应力、初始缺陷为关键参数,对其在褶皱产生和发展过程中的影响进行了研究。结果表明：随着薄膜厚度的增加,褶皱数量减少,幅值和波长变大,但面外位移与厚度的比值减小,因此厚度越小,褶皱对结构的不利影响越大；增大张拉预应力,可以延迟褶皱的出现,增强结构的面外稳定性,但是材料的强度安全储备会减少,因此应合理控制张拉预应力;初始缺陷主要影响到褶皱的位置,尤其是褶皱最先出现的位置,而对褶皱数量、波长、幅值等的影响不明显。
d.对褶皱发展不同阶段的结构动力特性进行了研究。结果表明：频率随剪切位移角的变化,也表现出三个典型阶段：初始阶段(频率下降),扩展阶段(频率波动上升)和稳定阶段(频率缓慢下降)。在稳定阶段,由于结构会发生二次屈曲,频率可能出现小幅波动。振型的变化与频率相比较为复杂,但总体趋势表现为与褶皱方向一致的振型增多。
With a large number of membrane structures used in the fields of building structures and spacecrafts, negative effects of wrinkles have aroused wide concern. The existences of wrinkles not only affect the surface accuracy of a structure, but also change its stress distributions and vibration performance and further affect the aerodynamic characteristics under wind load. Therefore, it is required that further researches be performed on the formation characteristics and the transition of wrinkles. Practical membranes are more complex and diverse in geometry than planar ones, and planar tension membrane is just one of the simplest structures, analysis on a simple planar membrane will contribute a lot to the attention on the common problems abstracted from membrane structures by excluding secondary factors and reveal the variation of mechanical properties following transition of wrinkles. Therefore, in this paper a planar membrane is mainly concerned to study the wrinkles and their influences on structures.
The content of this paper can be divided into two aspects of theory and numerical calculation:
(1) One part is on the theoretical analysis. Based on the stability theory, a new method of calculating critical compressive stress was proposed, in which the effect of tension stress along the wrinkling direction is considered. Afterwards, the formulas of wavelength and amplitude were easily obtained. Comparisons with the experiment results and the numerical results in the literatures show that the formulas given in this paper are valid, and have good accuracy.
(2) The other part is on the numerical analyses as the following:
a. A new method which divided the transition of the membrane wrinkles into three states was proposed. Generation and development of wrinkles were studied. The results show that:wrinkles appear first in the positions where compressive stress occurs earliest, and then expand to the middle part gradually until they are stable. The whole wrinkling process can be characterized by three typical stages:The Initial-Stage, The Expansion-Stage and The Stable-Stage. And the characteristics of each stage were studied. Through this part of study, the mechanism of wrinkles can be cognized. And the influence laws of mechanical properties affected by wrinkles can be mastered. And also, through this division, the degree of transition can be effectively measured; the wrinkles characters in a particular state can easily be studied and described.
b. Proposes and confirms a critical value to control wrinkles, in order to provide the quantitative basis to prevent the structural failure caused by the deformation and the wrinkles increases. The simulation researches on the shear rectangular tensile membrane show that:Wrinkles should be restricted to such an extent that the ratio between the out-plane displacement and the membrane thickness is less than1%. Otherwise, the out-plane deformation would increase rapidly, and cause the structure's failure.
c. The influence of thickness, initial prestress and initial imperfections on the wrinkles are studied. The results show that:with the increase of thickness, wrinkles decrease in number, but increase in wavelength and amplitude. However, the ratio of out-plane displacement to thickness decreases. Therefore, the smaller the thickness is, the larger the wrinkling impact is. Increase of the prestress can enhance the structure's out-plane stability and delay the appearance of wrinkles, but decrease the safety margin of structures. Therefore, the tension prestress should also be confined to a reasonable range. The initial imperfections mainly affect the location of wrinkles, especially the location where wrinkles appears first. But their influence on the wrinkling number, wavelength and amplitude is not obvious.
d. Dynamic characteristics of the structure at the different wrinkling stages are studied. The results show that:The frequency variation with shear displacement angle can also be characterized by three stages:The Initial-Stage in which the frequency is declining, The Expansion-Stage in which the frequency is raising fluctuates, and The Stable-Stage in which the frequency is declining again. In The Stable-Stage, because of the second-buckling of the membrane structure, the frequency appears to fluctuate. The change of the mode shape is much more complex than that of frequency. The mode shapes tend to increase along the wrinkles.
引文
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