考虑机械连接载荷和疲劳性能的装配结构拓扑优化设计方法
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摘要
针对工程中常见的多钉连接装配结构,提出了一种同时考虑钉载和疲劳性能的拓扑优化设计方法.一方面,将钉载约束考虑到装配结构的拓扑优化设计中,针对结构中大量的钉载约束,采用约束凝聚技术,简化了多约束问题灵敏度求解过程,提高了优化的计算效率.另一方面,将疲劳准则作为设计约束引入到拓扑优化问题中,为了避免因多钉连接结构建模方法引起的不真实应力状态对优化问题产生影响,采用组合单元对连接结构进行建模,用被连接件壳单元上的应力衡量结构疲劳性能,采用P范数凝聚方法对疲劳约束进行凝聚,在此基础上研究了拓扑优化设计中疲劳性能对结构拓扑形式和承载性能的影响.最后通过两个数值算例验证了所提方法的有效性.
The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners' static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners' failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q-p relaxation is used and p≥q≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.
The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners' static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners' failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q-p relaxation is used and p≥q≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.
引文
1 Desmorat B,Desmorat R.Topology optimization in damage governed low cycle fatigue.Comptes Rendus Mécanique,2008,336:448-453
2 Mrzyglod M.Multiaxial HCF and LCF constraints in topology optimization.In:Proceedings of the 9th International Conference on Multiaxial Fatigue and Fracture.Parma,2010.803-810
3 Mrzyglod M,Zielinski A P.Parametric structural optimization with respect to the multiaxial high-cycle fatigue criterion.Struct Multidisc Optim,2007,33:161-171
4 Holmberg E,Torstenfelt B,Klarbring A.Fatigue constrained topology optimization.Struct Multidisc Optim,2014,50:207-219
5 Collet M,Bruggi M,Duysinx P.Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance.Struct Multidisc Optim,2016,55:839-855
6 Oinonen A.Damage modelling procedure and fastener positioning optimization of adhesively reinforced frictional interfaces.Doctor Dissertation.Aalto:Aalto University,2011
7 Zhang Y,Taylor D.Sheet thickness effect of spot welds based on crack propagation.Engrg Fract Mech,2000,67:55-63
8 Xia L,Da D C,Yvonnet J.Topology optimization for maximizing the fracture resistance of quasi-brittle composites.Comput Methods Appl Mech Eng,2018,332:234-254
9 Bianchi G,Aglietti G S,Richardson G.Optimization of bolted joints connecting honeycomb panels.In:Proceedings of the 10th European Conference on Spacecraft Structures,Materials and Mechanical Testing.Berlin,2007.10-13
10 Liu P,Kang Z.Integrated topology optimization of multi-component structures considering connecting interface behavior.Comput Methods Appl Mech Eng,2018,341:851-887
11 Cao Y F,Zhu J H,Guo W J,et al.Structure topology optimization method for output loads precise control(in Chinese).Sci Sin Phys Mech Astron,2018,48:014606[曹吟锋,朱继宏,郭文杰,等.输出载荷精确控制的结构拓扑优化设计方法.中国科学:物理学力学天文学,2018,48:014606]
12 Zhu J H,Hou J,Zhang W H,et al.Structural topology optimization with constraints on multi-fastener joint loads.Struct Multidisc Optim,2014,50:561-571
13 Chickermane H.A layout optimization based theoretical framework for the design of multi-component structural systems.Doctor Dissertation.New Brunswick:The State University of New Jersey,1997
14 Ekh J,Sch?n J.Load transfer in multirow,single shear,composite-to-aluminium lap joints.Compos Sci Technol,2006,66:875-885
15 Bathe K J.Finite Element Procedures.Upper Saddle River:Prentice Hall,2006
16 Papadopoulos I.A comparative study of multiaxial high-cycle fatigue criteria for metals.Int J Fatigue,1997,19:219-235
17 Bends?e M P,Sigmund O.Topology Optimization:Theory,Methods and Applications.Berlin:Springer Berlin,2003
18 Cheng G,Guo X.ε-Relaxed approach in structural topology optimization.Struct Optim,1997,13:258-266
19 Bruggi M.On an alternative approach to stress constraints relaxation in topology optimization.Struct Multidisc Optim,2008,36:125-141
20 Xia Q,Shi T,Liu S,et al.A level set solution to the stress-based structural shape and topology optimization.Comput Struct,2012,90-91:55-64
21 Xia Q,Shi T,Liu S,et al.Shape and topology optimization for tailoring stress in a local region to enhance performance of piezoresistive sensors.Comput Struct,2013,114-115:98-105
22 Radovcic Y,Remouchamps A.BOSS QUATTRO:An open system for parametric design.Struct Multidisc Optim,2002,23:140-152
23 Svanberg K.A class of globally convergent optimization methods based on conservative convex separable approximations.Siam JOptim,2002,12:555-573
24 Zhu J H,Li Y,Zhang W H,et al.Shape preserving design with structural topology optimization.Struct Multidisc Optim,2016,53:893-906
2 Mrzyglod M.Multiaxial HCF and LCF constraints in topology optimization.In:Proceedings of the 9th International Conference on Multiaxial Fatigue and Fracture.Parma,2010.803-810
3 Mrzyglod M,Zielinski A P.Parametric structural optimization with respect to the multiaxial high-cycle fatigue criterion.Struct Multidisc Optim,2007,33:161-171
4 Holmberg E,Torstenfelt B,Klarbring A.Fatigue constrained topology optimization.Struct Multidisc Optim,2014,50:207-219
5 Collet M,Bruggi M,Duysinx P.Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance.Struct Multidisc Optim,2016,55:839-855
6 Oinonen A.Damage modelling procedure and fastener positioning optimization of adhesively reinforced frictional interfaces.Doctor Dissertation.Aalto:Aalto University,2011
7 Zhang Y,Taylor D.Sheet thickness effect of spot welds based on crack propagation.Engrg Fract Mech,2000,67:55-63
8 Xia L,Da D C,Yvonnet J.Topology optimization for maximizing the fracture resistance of quasi-brittle composites.Comput Methods Appl Mech Eng,2018,332:234-254
9 Bianchi G,Aglietti G S,Richardson G.Optimization of bolted joints connecting honeycomb panels.In:Proceedings of the 10th European Conference on Spacecraft Structures,Materials and Mechanical Testing.Berlin,2007.10-13
10 Liu P,Kang Z.Integrated topology optimization of multi-component structures considering connecting interface behavior.Comput Methods Appl Mech Eng,2018,341:851-887
11 Cao Y F,Zhu J H,Guo W J,et al.Structure topology optimization method for output loads precise control(in Chinese).Sci Sin Phys Mech Astron,2018,48:014606[曹吟锋,朱继宏,郭文杰,等.输出载荷精确控制的结构拓扑优化设计方法.中国科学:物理学力学天文学,2018,48:014606]
12 Zhu J H,Hou J,Zhang W H,et al.Structural topology optimization with constraints on multi-fastener joint loads.Struct Multidisc Optim,2014,50:561-571
13 Chickermane H.A layout optimization based theoretical framework for the design of multi-component structural systems.Doctor Dissertation.New Brunswick:The State University of New Jersey,1997
14 Ekh J,Sch?n J.Load transfer in multirow,single shear,composite-to-aluminium lap joints.Compos Sci Technol,2006,66:875-885
15 Bathe K J.Finite Element Procedures.Upper Saddle River:Prentice Hall,2006
16 Papadopoulos I.A comparative study of multiaxial high-cycle fatigue criteria for metals.Int J Fatigue,1997,19:219-235
17 Bends?e M P,Sigmund O.Topology Optimization:Theory,Methods and Applications.Berlin:Springer Berlin,2003
18 Cheng G,Guo X.ε-Relaxed approach in structural topology optimization.Struct Optim,1997,13:258-266
19 Bruggi M.On an alternative approach to stress constraints relaxation in topology optimization.Struct Multidisc Optim,2008,36:125-141
20 Xia Q,Shi T,Liu S,et al.A level set solution to the stress-based structural shape and topology optimization.Comput Struct,2012,90-91:55-64
21 Xia Q,Shi T,Liu S,et al.Shape and topology optimization for tailoring stress in a local region to enhance performance of piezoresistive sensors.Comput Struct,2013,114-115:98-105
22 Radovcic Y,Remouchamps A.BOSS QUATTRO:An open system for parametric design.Struct Multidisc Optim,2002,23:140-152
23 Svanberg K.A class of globally convergent optimization methods based on conservative convex separable approximations.Siam JOptim,2002,12:555-573
24 Zhu J H,Li Y,Zhang W H,et al.Shape preserving design with structural topology optimization.Struct Multidisc Optim,2016,53:893-906
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