建筑膜结构的找形与裁剪分析及膜内张力的超声波测试方法研究
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摘要
现代膜结构是在新型膜材料基础上发展起来的一种新型结构形式,因其自重轻、施工周期短、透光性好、丰富的建筑表现力等优点而在体育建筑、公共建筑等方面得到了广泛应用。膜材料是一种柔性的,具有强非线性和各向异性的材料,膜结构的设计在很大程度上取决于膜材料的性能,了解膜材料的特性对于膜结构的设计至关重要。建筑膜结构由柔性薄膜张拉而成,依赖于结构的几何曲面和膜内张力来提供必需的刚度,膜结构设计的首要步骤是找形分析,其目的是找出满足建筑要求的空间形状及与之对应的张力分布。裁剪分析是膜结构特有的一个分析步骤,其目的是将由找形得到的预应力状态的空间曲面进行剖分、转换成无应力的平面下料图,以便将平面膜材热合成整体,再施加预应力以张成设计曲面。合适的膜内张力是膜面能够张成并承受荷载的保证,方便快捷的对膜内张力进行现场测量是保证膜结构施工质量的要求。
针对上述几点,本文的主要内容如下:
1.概述了建筑膜结构的发展历史及其应用现状,对膜结构的设计内容及其国内外研究现状进行了详尽的论述。
2.对一种PVDF涂层的聚酯纤维膜材进行实验研究。制作了经向、纬线和45°斜向的条状单轴试件和十字形双轴实验试件,分别进行了单轴拉伸和双轴拉伸实验,其中双轴实验采用了自行设计的实验装置。通过单轴实验确定了膜材不同方向的单轴拉伸强度,全程拉伸曲线。双轴拉伸实验则得到了膜材的弹性模量和泊松比等参数,并深入了解膜材的变形性能,全面理解了膜材的材料特性,为后续的结构分析奠定了基础。
3.从板壳力学的平衡方程出发,证明了膜内各点处处相等的膜内应力分布将得到最小曲面,而平衡应力分布则得到平衡曲面。
4.应用动力阻尼的动力松弛法进行了膜结构的找形分析。动力松弛法解几何非线性问题的一个显著优点是不需要计算结构的整体刚度矩阵和求解整体刚度矩阵方程,然而它所需要的迭代次数较多。本文在找形过程中根据结构位形的变化重新计算节点刚度、质量,不断调整计算参数,从而加快计算的收敛。算例说明,用改进后的动力松弛法进行膜结构的找形分析,与在整个找形过程中采用同一计算参数相比较,大大减少了迭代次数。由于忽略膜内剪切刚度,找形过程中单元变形较大,可通过结点坐标多步提升到位来解决问题。
5.本文给出了两种膜结构曲面模拟的方法,通过对找形得到的散乱节点进行分片二元三次样条插值,得到整体C0连续和C1连续的光滑曲面,适用于任意多边形区域。两种插值方法均能给出膜曲面的满意表现。C1插值曲面的误差远小于C0插值曲面。对两种插值方法,模拟曲面的误差均随着初始网格尺度与平面总尺寸的比值减小而下降,在初始网格尺度与平面总尺寸的比值小于1/8之后,拟合曲面的精度变化随该比值的下降变化值逐渐不明显。
6.曲面上的测地线与平面上的直线有许多相似的性质,测地线的直线性质使其成为最适宜的也是目前应用最为广泛的裁剪缝。可以证明,连接平滑曲面上任意两点的弹性细丝当拉紧时具有测地线的形状。本文在曲面上指定两点间引入弹性索,使其在曲面上自由滑移,并用动力松弛法寻找其平衡位置,即得测地线轨迹。
7.采用测地线划分曲面,应用最小极值法进行曲面的展开。首先将曲面离散为空间三角形网格,假设曲面已近似展开为平面,调整展开平面中各节点的位置,使平面网格中各三角形的边长曲面网格中对应的边长之差最小,从而求得空间曲面的平面近似展开。本文将上述展开过程归纳为一个无约束的极值问题,并用蒙特卡洛法求解非线性方程。对于曲面上测地线的寻找和空间曲面展开分别给出了算例,用可展曲面圆柱面验证提出方法的正确性,并应用提出的方法给出了一个菱形马鞍膜面的裁剪样式。
As a newly developed structure, membrane structures are widely used in gymnasiums and public facilities, owing to the excellent characteristic. Behaviors of membrane structures are depended to properties of membrane materials, which is flexible, non-linear and anisotropic. Stiffness of membrane structures is provided by surface curve and pre-stresses, therefore form-finding is the first and foremost step in design of membrane structures. In order to obtaining space surfaces from plane membrane materials, patterning is a peculiarly procedure for membrane structure design. Since proper pre-stress ensures the erection and safety under loads, measurement of membrane tension is a necessity for quality control.
According to the aforementioned points, main contents of this dissertation are as follows:
1. History and application of membrane structures were reviewed , and main steps for design of membrane structures and the state of the art were summarized.
2. A kind of PVDF membrane material was experimentally studied. Sample strips parallel to the warp, or fill direction, as well as those through 45°angle direction were tailored and tested. Also a kind of crossed sample was tested by a self-made biaxial test equipment. Mono-axis tests give strip strengths and stress-strain curves of the material, while biaxial tests yields elastic module and Poisson’s ratio. These experiments made materials’properties clear and laid foundations for the following analysis.
3. A conclusion was induced from equilibrium equations of shells as follows: stress distribution in membrane structures can be either homogeneous and isotropic, resulting in a minimum surface or inhomogeneous and anisotropic, resulting in a equilibrium surface.
4. Form finding of membrane structures was carried out by dynamic relaxation. As one of the most frequently used form finding method for membrane structures, dynamic relaxation features the facility of no need to assemble and solve structure stiffness equations, while the cost is the relatively numerous iterations. In this paper dynamic relaxation was modified to accelerate the convergence. During the form finding procedure the calculating parameters were continuously adjusted according to changes of the structure, and the iteration steps to convergence were greatly reduced comparing with those without parameter adjusting. The excessive distortion of elements, which may occur due to omitting of the in-plane shear stiffness can be overcame by sequential designation of node coordinates.
5. Two simulating procedures for discrete membrane structures were introduced. By piecewise interpolating of the discrete surface resulted from form finding procedures, continuous smooth curved surfaces were obtained. Samples showed that though both of the simulating processes led to satisfying presentation of curved membrane surfaces, discrepancies of the simulated surfaces from the standard coordinates to the C1 surfaces were much less than that to the C0 surfaces. Discrepancies decreased with the reduce of the grid/span ratio, while as the ratio was less than 1/8 , the discrepancies gradually diminished.
6. Geodesic of surfaces is similar to straight lines in planes, and thus makes geodesics the mostly frequently used dividing lines in patterning of membranes. It is proved that geodesics can be produced by stretch elastic strings along a smooth surface. Equilibrium of stretched strings were found by dynamic relaxation, thus gave tracks of geodesics.
7. Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method. Firstly, curved surfaces were discretized into triangles, and a plane mesh was supposed to be the developed surface, then nodes in the plane mesh were adjusted to minimize distance differences between plane and space surface. The aforementioned procedures were summarized into a non-boundary extremum problem, and the non-linear equations were solved by Monte Carlo iterations. Examples were given to illustrate the stated procedures, and patterning of a rhombic saddle was provided.
针对上述几点,本文的主要内容如下:
1.概述了建筑膜结构的发展历史及其应用现状,对膜结构的设计内容及其国内外研究现状进行了详尽的论述。
2.对一种PVDF涂层的聚酯纤维膜材进行实验研究。制作了经向、纬线和45°斜向的条状单轴试件和十字形双轴实验试件,分别进行了单轴拉伸和双轴拉伸实验,其中双轴实验采用了自行设计的实验装置。通过单轴实验确定了膜材不同方向的单轴拉伸强度,全程拉伸曲线。双轴拉伸实验则得到了膜材的弹性模量和泊松比等参数,并深入了解膜材的变形性能,全面理解了膜材的材料特性,为后续的结构分析奠定了基础。
3.从板壳力学的平衡方程出发,证明了膜内各点处处相等的膜内应力分布将得到最小曲面,而平衡应力分布则得到平衡曲面。
4.应用动力阻尼的动力松弛法进行了膜结构的找形分析。动力松弛法解几何非线性问题的一个显著优点是不需要计算结构的整体刚度矩阵和求解整体刚度矩阵方程,然而它所需要的迭代次数较多。本文在找形过程中根据结构位形的变化重新计算节点刚度、质量,不断调整计算参数,从而加快计算的收敛。算例说明,用改进后的动力松弛法进行膜结构的找形分析,与在整个找形过程中采用同一计算参数相比较,大大减少了迭代次数。由于忽略膜内剪切刚度,找形过程中单元变形较大,可通过结点坐标多步提升到位来解决问题。
5.本文给出了两种膜结构曲面模拟的方法,通过对找形得到的散乱节点进行分片二元三次样条插值,得到整体C0连续和C1连续的光滑曲面,适用于任意多边形区域。两种插值方法均能给出膜曲面的满意表现。C1插值曲面的误差远小于C0插值曲面。对两种插值方法,模拟曲面的误差均随着初始网格尺度与平面总尺寸的比值减小而下降,在初始网格尺度与平面总尺寸的比值小于1/8之后,拟合曲面的精度变化随该比值的下降变化值逐渐不明显。
6.曲面上的测地线与平面上的直线有许多相似的性质,测地线的直线性质使其成为最适宜的也是目前应用最为广泛的裁剪缝。可以证明,连接平滑曲面上任意两点的弹性细丝当拉紧时具有测地线的形状。本文在曲面上指定两点间引入弹性索,使其在曲面上自由滑移,并用动力松弛法寻找其平衡位置,即得测地线轨迹。
7.采用测地线划分曲面,应用最小极值法进行曲面的展开。首先将曲面离散为空间三角形网格,假设曲面已近似展开为平面,调整展开平面中各节点的位置,使平面网格中各三角形的边长曲面网格中对应的边长之差最小,从而求得空间曲面的平面近似展开。本文将上述展开过程归纳为一个无约束的极值问题,并用蒙特卡洛法求解非线性方程。对于曲面上测地线的寻找和空间曲面展开分别给出了算例,用可展曲面圆柱面验证提出方法的正确性,并应用提出的方法给出了一个菱形马鞍膜面的裁剪样式。
As a newly developed structure, membrane structures are widely used in gymnasiums and public facilities, owing to the excellent characteristic. Behaviors of membrane structures are depended to properties of membrane materials, which is flexible, non-linear and anisotropic. Stiffness of membrane structures is provided by surface curve and pre-stresses, therefore form-finding is the first and foremost step in design of membrane structures. In order to obtaining space surfaces from plane membrane materials, patterning is a peculiarly procedure for membrane structure design. Since proper pre-stress ensures the erection and safety under loads, measurement of membrane tension is a necessity for quality control.
According to the aforementioned points, main contents of this dissertation are as follows:
1. History and application of membrane structures were reviewed , and main steps for design of membrane structures and the state of the art were summarized.
2. A kind of PVDF membrane material was experimentally studied. Sample strips parallel to the warp, or fill direction, as well as those through 45°angle direction were tailored and tested. Also a kind of crossed sample was tested by a self-made biaxial test equipment. Mono-axis tests give strip strengths and stress-strain curves of the material, while biaxial tests yields elastic module and Poisson’s ratio. These experiments made materials’properties clear and laid foundations for the following analysis.
3. A conclusion was induced from equilibrium equations of shells as follows: stress distribution in membrane structures can be either homogeneous and isotropic, resulting in a minimum surface or inhomogeneous and anisotropic, resulting in a equilibrium surface.
4. Form finding of membrane structures was carried out by dynamic relaxation. As one of the most frequently used form finding method for membrane structures, dynamic relaxation features the facility of no need to assemble and solve structure stiffness equations, while the cost is the relatively numerous iterations. In this paper dynamic relaxation was modified to accelerate the convergence. During the form finding procedure the calculating parameters were continuously adjusted according to changes of the structure, and the iteration steps to convergence were greatly reduced comparing with those without parameter adjusting. The excessive distortion of elements, which may occur due to omitting of the in-plane shear stiffness can be overcame by sequential designation of node coordinates.
5. Two simulating procedures for discrete membrane structures were introduced. By piecewise interpolating of the discrete surface resulted from form finding procedures, continuous smooth curved surfaces were obtained. Samples showed that though both of the simulating processes led to satisfying presentation of curved membrane surfaces, discrepancies of the simulated surfaces from the standard coordinates to the C1 surfaces were much less than that to the C0 surfaces. Discrepancies decreased with the reduce of the grid/span ratio, while as the ratio was less than 1/8 , the discrepancies gradually diminished.
6. Geodesic of surfaces is similar to straight lines in planes, and thus makes geodesics the mostly frequently used dividing lines in patterning of membranes. It is proved that geodesics can be produced by stretch elastic strings along a smooth surface. Equilibrium of stretched strings were found by dynamic relaxation, thus gave tracks of geodesics.
7. Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method. Firstly, curved surfaces were discretized into triangles, and a plane mesh was supposed to be the developed surface, then nodes in the plane mesh were adjusted to minimize distance differences between plane and space surface. The aforementioned procedures were summarized into a non-boundary extremum problem, and the non-linear equations were solved by Monte Carlo iterations. Examples were given to illustrate the stated procedures, and patterning of a rhombic saddle was provided.
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