复合材料桁架弯曲特性与非线性约束优化设计
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摘要
新型航天器对支撑结构部件提出了超轻质、大跨度、可伸缩需求。本文以开发大型超轻质支撑结构为目的,提出了一类新的全复合材料桁架结构——三角形截面复合材料整体桁架结构。该复合材料桁架结构单元不含接头,具有均一中空尺寸,不同截面尺寸的桁架可以套装在一起实现伸缩。本文围绕该复合材料桁架结构单元的轻量化,开展了结构构型设计、整体制备技术与弯曲性能表征研究;根据该复合材料桁架结构的弯曲特性,系统地开展了非线性结构响应约束下的多参数优化设计方法研究。主要研究工作包括:
开展了三角形截面复合材料整体桁架结构单元的基本构型设计研究。利用计算机模拟获得纤维缠绕工艺可实现的四种缠绕线型,采用有限元分析方法从中优选出具有最佳结构质量效率及结构刚度/质量比的Ⅱ型桁架构型。将该构型三角形截面复合材料整体桁架与复合材料等代桁架的弯曲性能进行比较。结果表明,在悬臂梁弯曲载荷状况及相同几何尺寸约束条件下,该三角形截面桁架弯曲刚度和弯曲刚度/质量比分别为等代桁架的189%和345%。
开展了桁架结构整体制备工艺方法研究。采用连续纤维缠绕工艺制备该构型复合材料整体桁架。设计并制造了由旋转轴和可拆卸式支撑板为主要构件的缠绕芯模。采用纤维束绑束方法提高桁架肋条的纤维体积分数,从而提高其承载能力,达到更高的载荷/质量比。确定了以环氧树脂CYD-128和固化剂对二氨基二苯基甲烷DDM或二乙烯三胺DETA的基体材料体系。对该工艺制得的复合材料整体桁架进行了工艺质量表征。结果表明,该工艺制得的复合材料桁架肋条直径离散系数为6.94%,玻璃纤维/环氧和碳纤维/环氧桁架肋条的纤维体积含量分别为63.44%和55.39%,拉伸模量分别为45.83 GPa和113.42 GPa,拉伸强度分别为747.58 MPa和1049.49 MPa,工艺质量及力学性能均达到同类复合材料制品的较高水平。
开展了整体桁架结构的弯曲性能表征研究。设计了三点弯曲实验方案并对桁架的弯曲性能进行实验表征。结果表明,桁架在三点弯曲载荷下表现出明显的非线性屈服行为特征。桁架中截面载荷-位移曲线的屈服点可用于表征桁架的结构刚度和屈服载荷。建立了该桁架结构三点弯曲载荷下的非线性有限元分析模型,将计算模拟结果与实验结果进行了比较验证。结果表明,有限元分析结果与实验结果间的最大误差不超过10%,该有限元模型能较准确地预测复合材料整体桁架结构在弯曲载荷下的屈服载荷及相应位移。
利用该有限元分析模型系统开展了桁架几何参数与屈服载荷、结构刚度、刚度/质量比和载荷/质量比之间关系的研究。结果表明,桁架截面外接圆直径是决定桁架结构刚度的关键几何参数;间隔数是桁架屈服载荷的决定性几何参数;螺旋向肋条直径是桁架总质量及承载效率的决定性几何参数,并且螺旋向肋条直径的变化将引起载荷-位移曲线屈服点后桁架刚度的变化。
开展了复合材料整体桁架的失效模式研究。在屈服载荷下,复合材料桁架肋条的轴向拉应力、压应力及截面剪应力均远小于其强度值,因此不会发生强度控制的破坏失效。肋条剪应力及弯矩均较小,主要受力状态为拉、压应力,因此该构型复合材料整体桁架结构可以近似认为是拉伸主导型结构。桁架最终的失效模式为结构刚度控制的局部屈曲以及最终的整体失稳。
开展了非线性结构响应约束下的多参数优化设计研究。以结构质量为优化目标,将桁架三点弯曲载荷下的非线性结构响应量——载荷-位移曲线屈服点对应的载荷和位移作为约束条件,同时对桁架的四个主要几何参数进行优化。采用响应面法构造了两个非线性结构响应量(屈服载荷及对应位移)与四个设计变量间的二次响应面模型。将该响应面模型作为约束函数引入优化程序,经优化求解获得总质量最小的最优化设计结果,并对优化设计结果进行了有限元分析验证和进一步的实验验证。研究结果表明,用该方法获得的响应面模型函数预测的结构响应值与有限元分析结果间的误差不超过15%。根据优化设计结果制得的复合材料桁架在三点弯曲载荷下的屈服载荷及相应位移均满足设计要求,与优化结果的误差不超过7%。该优化方法能对四个设计参数同时进行优化,优化设计结果更趋合理。
开展了含制造缺陷及尺寸误差桁架承载能力评估的研究。考察了桁架不同位置肋条的断裂失效对桁架承载能力的影响。结果表明,纵向肋条断裂失效将导致桁架屈服载荷及整体结构刚度的显著降低。螺旋向肋条断裂失效对桁架结构刚度无明显影响,但会导致桁架承载能力(屈服载荷)降低。其中,桁架中截面附近承受较大载荷的螺旋向肋条失效后,桁架承载能力将降低至完好桁架的85%以下。采用几何点偏移的方法研究不同位置和方向的制造尺寸误差对桁架弯曲性能的影响,确定了桁架不同位置几何点沿不同方向的尺寸误差容限。结果表明,10 mm以下的几何尺寸误差对桁架结构刚度无明显影响,但对桁架承载能力有显著影响。其中,当桁架中截面附近几何点的尺寸误差大于1 mm时,桁架承载能力将降低至完好桁架的85%以下,即桁架中截面附近几何点的尺寸误差容限为1 mm。
Ultra-lightweight, long span and deployable supporting structural components are demanded by new spacecraft. In this paper, a new composite truss structure with triangular cross section is developed for large-scale aerospace applications. This composite truss structure is integrally manufactured by filament winding and no joints are included. Inner space with uniform triangular cross section is big enough to allow several trusses with different cross section dimensions being assembled and the deployable mechanism can be achieved in this way. Studies on configuration design, integrally manufacture, flexural performance and design optimization of this composite truss structural element are conducted in this paper. The main work includes:
Truss structure with triangular cross section is chosen as the fundamental configuration. Four detail configurations which are achievable by filament winding process are obtained by CAD (Computer Assisted Design). Mass efficiency and stiffness to mass ratio of the four configurations are compared by finite element analysis and the final truss configuration (typeⅡ) is obtained. Flexural performance of the composite truss with triangular cross section is compared with composite IsoTruss? structures. The results show that, under the same geometry dimensions constraints and cantilever bending condition, the flexural stiffness and flexural stiffness to mass ratio of the composite truss structure with triangular cross section are 189% and 345% of the IsoTruss? structure respectively.
Continuous filament winding process is employed to integrally manufacture the composite truss. The mandrel consists of core pipe and dismountable supporting panel. Composite ribs are consolidated by high strength glass fiber yarn typing which lead to higher fiber volume content, load to mass ratio and better loading capacity. Epoxy resin CYD-128 and curing agent 4, 4’-diaminodiphenylmethane (DDM) or Diethylenetriamine (DETA) are used as resin matrix. Diameter, density, fiber volume content of the composite ribs were measured and the tension properties of the ribs were tested to evaluate the manufacture quality.The results show that, the variation coefficient of truss rib diameter is 6.94%. Average fiber volume content of glass fiber/epoxy and carbon fiber/epoxy helical rib is 63.44% and 55.39% respectively. Tension modulus of of glass fiber/epoxy and carbon fiber/epoxy helical rib is 45.83 GPa and 113.42 GPa. Tension strength of of glass fiber/epoxy and carbon fiber/epoxy helical rib is 747.58 MPa and 1049.49 MPa respectively. Compared to the composite structure fabricated by other process, composite truss manufactured by this way has good manufacture quality and mechanical properties.
Flexural performance of this composite truss structures is experimentally investigated under three point bending. Local buckling and global buckling of the truss specimen can be observed during the test. A yield point is included in the load-displacement curves of middle cross section of the composite truss. Yield load and structural stiffness of the composite truss can be derived from the yield point data. Nonlinear finite element analysis is also performed to investigate the bending behavior of the composite truss. The results show that the difference between experimental results and numerical results is no more than 10%. The finite element model can be employed to predict the yield load and displacement of this composite truss structure with acceptable accuracy under three point bending.
Sensitivity analysis is conducted to determine the effects of the four geometric parameters on the flexural performance of this truss structure. The results that, the outer diameter and bay number of this composite truss structure are critical geometric parameters underpinning the structural stiffness and yield load respectively. Total mass and load efficiency of the composite truss is sensitive to the variation of helical rib diameter. Among the four parameters, helical rib diameter is the only one that can change the structural stiffness of the composite truss after the yield point of load-displacement curves.
Stress of the composite ribs show that, axial tensile stress, axial compressive stress and shear stress are far less to the strength. Strength-controlled failure will not happen. As the shear stress and bending moment of all the truss ribs are very low and the main stresses on the ribs are axial tensile or compressive stress, this composite truss structure can be approximately considered as stretching-dominated structure. The failure mode of the composite truss structure is local rib buckling and global buckling controlled by structural stiffness.
Multi-parameters optimization of the composite truss structure is performed under the nonlinear structural responses. Total weight of the composite truss is taken as optimization object. Nonlinear structural responses, yield load and displacement, are taken as constraints. Four geometric parameters are taken as design variables to be optimized. Response surface methodology is employed to construct the constraint functions between the two nonlinear structural responses (yield load and displacement) and four design parameters. Matlab Optimization ToolboxTM is used to perform the optimization. Optimal results has been validated by both finite element analysis and experiment. The results show that, error of the yield load and displacement predicted by response surface model function is no more than 15%. Flexural performance of the composite truss specimen fabricated based on the optimal design meet the design requirements. The difference of yield load and displacement between experimental result and optimal design is no more than 7%. As four parameters can be taken as design variables simultaneously, the optimal result obtained by this method is more reasonable.
Effects of local rib damage on the flexural performance of composite truss are further investigated by individually removing the rib. The results show that structural stiffness and yield load of the composite truss will be distinctly decrease by longitudinal rib damage. Damage of helical rib with high stress near the middle cross section will lead to the decrease of yield load and the residual yield load will be less than 85% of the intact truss. Effects of geometric dimension deviation on flexural performance of the composite truss are investigated by geometric keypoint offset and the dimensional deviation tolerance for each geometric keypoint is obtained. The results show that dimensional deviation less than 10 mm almost has no effects on the structural stiffness of the composite truss. When the dimensional deviation of the geometric keypoint near the middle cross section is more than 1 mm, the residual yield load of the composite truss will be less than 85% of the intact truss. Dimensional deviation tolerance of these geometric keypoints is 1 mm.
开展了三角形截面复合材料整体桁架结构单元的基本构型设计研究。利用计算机模拟获得纤维缠绕工艺可实现的四种缠绕线型,采用有限元分析方法从中优选出具有最佳结构质量效率及结构刚度/质量比的Ⅱ型桁架构型。将该构型三角形截面复合材料整体桁架与复合材料等代桁架的弯曲性能进行比较。结果表明,在悬臂梁弯曲载荷状况及相同几何尺寸约束条件下,该三角形截面桁架弯曲刚度和弯曲刚度/质量比分别为等代桁架的189%和345%。
开展了桁架结构整体制备工艺方法研究。采用连续纤维缠绕工艺制备该构型复合材料整体桁架。设计并制造了由旋转轴和可拆卸式支撑板为主要构件的缠绕芯模。采用纤维束绑束方法提高桁架肋条的纤维体积分数,从而提高其承载能力,达到更高的载荷/质量比。确定了以环氧树脂CYD-128和固化剂对二氨基二苯基甲烷DDM或二乙烯三胺DETA的基体材料体系。对该工艺制得的复合材料整体桁架进行了工艺质量表征。结果表明,该工艺制得的复合材料桁架肋条直径离散系数为6.94%,玻璃纤维/环氧和碳纤维/环氧桁架肋条的纤维体积含量分别为63.44%和55.39%,拉伸模量分别为45.83 GPa和113.42 GPa,拉伸强度分别为747.58 MPa和1049.49 MPa,工艺质量及力学性能均达到同类复合材料制品的较高水平。
开展了整体桁架结构的弯曲性能表征研究。设计了三点弯曲实验方案并对桁架的弯曲性能进行实验表征。结果表明,桁架在三点弯曲载荷下表现出明显的非线性屈服行为特征。桁架中截面载荷-位移曲线的屈服点可用于表征桁架的结构刚度和屈服载荷。建立了该桁架结构三点弯曲载荷下的非线性有限元分析模型,将计算模拟结果与实验结果进行了比较验证。结果表明,有限元分析结果与实验结果间的最大误差不超过10%,该有限元模型能较准确地预测复合材料整体桁架结构在弯曲载荷下的屈服载荷及相应位移。
利用该有限元分析模型系统开展了桁架几何参数与屈服载荷、结构刚度、刚度/质量比和载荷/质量比之间关系的研究。结果表明,桁架截面外接圆直径是决定桁架结构刚度的关键几何参数;间隔数是桁架屈服载荷的决定性几何参数;螺旋向肋条直径是桁架总质量及承载效率的决定性几何参数,并且螺旋向肋条直径的变化将引起载荷-位移曲线屈服点后桁架刚度的变化。
开展了复合材料整体桁架的失效模式研究。在屈服载荷下,复合材料桁架肋条的轴向拉应力、压应力及截面剪应力均远小于其强度值,因此不会发生强度控制的破坏失效。肋条剪应力及弯矩均较小,主要受力状态为拉、压应力,因此该构型复合材料整体桁架结构可以近似认为是拉伸主导型结构。桁架最终的失效模式为结构刚度控制的局部屈曲以及最终的整体失稳。
开展了非线性结构响应约束下的多参数优化设计研究。以结构质量为优化目标,将桁架三点弯曲载荷下的非线性结构响应量——载荷-位移曲线屈服点对应的载荷和位移作为约束条件,同时对桁架的四个主要几何参数进行优化。采用响应面法构造了两个非线性结构响应量(屈服载荷及对应位移)与四个设计变量间的二次响应面模型。将该响应面模型作为约束函数引入优化程序,经优化求解获得总质量最小的最优化设计结果,并对优化设计结果进行了有限元分析验证和进一步的实验验证。研究结果表明,用该方法获得的响应面模型函数预测的结构响应值与有限元分析结果间的误差不超过15%。根据优化设计结果制得的复合材料桁架在三点弯曲载荷下的屈服载荷及相应位移均满足设计要求,与优化结果的误差不超过7%。该优化方法能对四个设计参数同时进行优化,优化设计结果更趋合理。
开展了含制造缺陷及尺寸误差桁架承载能力评估的研究。考察了桁架不同位置肋条的断裂失效对桁架承载能力的影响。结果表明,纵向肋条断裂失效将导致桁架屈服载荷及整体结构刚度的显著降低。螺旋向肋条断裂失效对桁架结构刚度无明显影响,但会导致桁架承载能力(屈服载荷)降低。其中,桁架中截面附近承受较大载荷的螺旋向肋条失效后,桁架承载能力将降低至完好桁架的85%以下。采用几何点偏移的方法研究不同位置和方向的制造尺寸误差对桁架弯曲性能的影响,确定了桁架不同位置几何点沿不同方向的尺寸误差容限。结果表明,10 mm以下的几何尺寸误差对桁架结构刚度无明显影响,但对桁架承载能力有显著影响。其中,当桁架中截面附近几何点的尺寸误差大于1 mm时,桁架承载能力将降低至完好桁架的85%以下,即桁架中截面附近几何点的尺寸误差容限为1 mm。
Ultra-lightweight, long span and deployable supporting structural components are demanded by new spacecraft. In this paper, a new composite truss structure with triangular cross section is developed for large-scale aerospace applications. This composite truss structure is integrally manufactured by filament winding and no joints are included. Inner space with uniform triangular cross section is big enough to allow several trusses with different cross section dimensions being assembled and the deployable mechanism can be achieved in this way. Studies on configuration design, integrally manufacture, flexural performance and design optimization of this composite truss structural element are conducted in this paper. The main work includes:
Truss structure with triangular cross section is chosen as the fundamental configuration. Four detail configurations which are achievable by filament winding process are obtained by CAD (Computer Assisted Design). Mass efficiency and stiffness to mass ratio of the four configurations are compared by finite element analysis and the final truss configuration (typeⅡ) is obtained. Flexural performance of the composite truss with triangular cross section is compared with composite IsoTruss? structures. The results show that, under the same geometry dimensions constraints and cantilever bending condition, the flexural stiffness and flexural stiffness to mass ratio of the composite truss structure with triangular cross section are 189% and 345% of the IsoTruss? structure respectively.
Continuous filament winding process is employed to integrally manufacture the composite truss. The mandrel consists of core pipe and dismountable supporting panel. Composite ribs are consolidated by high strength glass fiber yarn typing which lead to higher fiber volume content, load to mass ratio and better loading capacity. Epoxy resin CYD-128 and curing agent 4, 4’-diaminodiphenylmethane (DDM) or Diethylenetriamine (DETA) are used as resin matrix. Diameter, density, fiber volume content of the composite ribs were measured and the tension properties of the ribs were tested to evaluate the manufacture quality.The results show that, the variation coefficient of truss rib diameter is 6.94%. Average fiber volume content of glass fiber/epoxy and carbon fiber/epoxy helical rib is 63.44% and 55.39% respectively. Tension modulus of of glass fiber/epoxy and carbon fiber/epoxy helical rib is 45.83 GPa and 113.42 GPa. Tension strength of of glass fiber/epoxy and carbon fiber/epoxy helical rib is 747.58 MPa and 1049.49 MPa respectively. Compared to the composite structure fabricated by other process, composite truss manufactured by this way has good manufacture quality and mechanical properties.
Flexural performance of this composite truss structures is experimentally investigated under three point bending. Local buckling and global buckling of the truss specimen can be observed during the test. A yield point is included in the load-displacement curves of middle cross section of the composite truss. Yield load and structural stiffness of the composite truss can be derived from the yield point data. Nonlinear finite element analysis is also performed to investigate the bending behavior of the composite truss. The results show that the difference between experimental results and numerical results is no more than 10%. The finite element model can be employed to predict the yield load and displacement of this composite truss structure with acceptable accuracy under three point bending.
Sensitivity analysis is conducted to determine the effects of the four geometric parameters on the flexural performance of this truss structure. The results that, the outer diameter and bay number of this composite truss structure are critical geometric parameters underpinning the structural stiffness and yield load respectively. Total mass and load efficiency of the composite truss is sensitive to the variation of helical rib diameter. Among the four parameters, helical rib diameter is the only one that can change the structural stiffness of the composite truss after the yield point of load-displacement curves.
Stress of the composite ribs show that, axial tensile stress, axial compressive stress and shear stress are far less to the strength. Strength-controlled failure will not happen. As the shear stress and bending moment of all the truss ribs are very low and the main stresses on the ribs are axial tensile or compressive stress, this composite truss structure can be approximately considered as stretching-dominated structure. The failure mode of the composite truss structure is local rib buckling and global buckling controlled by structural stiffness.
Multi-parameters optimization of the composite truss structure is performed under the nonlinear structural responses. Total weight of the composite truss is taken as optimization object. Nonlinear structural responses, yield load and displacement, are taken as constraints. Four geometric parameters are taken as design variables to be optimized. Response surface methodology is employed to construct the constraint functions between the two nonlinear structural responses (yield load and displacement) and four design parameters. Matlab Optimization ToolboxTM is used to perform the optimization. Optimal results has been validated by both finite element analysis and experiment. The results show that, error of the yield load and displacement predicted by response surface model function is no more than 15%. Flexural performance of the composite truss specimen fabricated based on the optimal design meet the design requirements. The difference of yield load and displacement between experimental result and optimal design is no more than 7%. As four parameters can be taken as design variables simultaneously, the optimal result obtained by this method is more reasonable.
Effects of local rib damage on the flexural performance of composite truss are further investigated by individually removing the rib. The results show that structural stiffness and yield load of the composite truss will be distinctly decrease by longitudinal rib damage. Damage of helical rib with high stress near the middle cross section will lead to the decrease of yield load and the residual yield load will be less than 85% of the intact truss. Effects of geometric dimension deviation on flexural performance of the composite truss are investigated by geometric keypoint offset and the dimensional deviation tolerance for each geometric keypoint is obtained. The results show that dimensional deviation less than 10 mm almost has no effects on the structural stiffness of the composite truss. When the dimensional deviation of the geometric keypoint near the middle cross section is more than 1 mm, the residual yield load of the composite truss will be less than 85% of the intact truss. Dimensional deviation tolerance of these geometric keypoints is 1 mm.
引文
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