Research On Topology Optimization Method For Compliant Mechanisms With Composites Laminated Plates

Compliant mechanisms are the type of mechanisms which can achieve movement and transform force by virtue of elastic deformation.They are widely used in field of MEMS,Aviation and aerospace,medical instruments with features of no hinge and friction,no necessity of assembly and lubrication,easy fabrication and lightweight,and so on.Therefore,they have become an important branch in the research field of modern mechanisms and method of topology optimization for compliant mechanisms is the focus of research fields.At present,design methods of compliant mechanisms are mainly based on topology optimization of compliant mechanisms with isotropic materials.Because mechanisms with isotropic materials don't distribute reasonably the stiffness and stress according to the characteristics of their topology shapes,deformation and loading states,there is the limitation of deformation and bearing capacity.For this reason,design methods of topology optimization for compliant mechanisms are researched using the anisotropic features of composites and composite laminate theory in this paper.The optimization method of combining fiber orientations(paths)and topology shapes of compliant mechanisms with constant and variable stiffness laminated plates is built by investigating and revealing influences of fiber orientations(paths)on deformation stiffness,stress properties and topology shapes.Common optimization of material design and topology design for mechanisms are achieved using the method.Finally,compliant leading edge and trailing edge of morphing wing are designed and experiment investigated.The main research work of this paper is as follows:(1)Topology design and analysis of compliant mechanisms with constant stiffness composites laminated plates.Based on the classical lamination theory and SIMP model,an equivalent constitutive relation and topology optimization method of compliant mechanisms with constant stiffness lamination plates are built.Compliant inverters and grippers are taken as numerical examples to design topology shapes and reveal the influences of fiber orientations on topology shapes,deformation and bearing capability by comparing their deformation and stress levels.The results show that materials distribution in hinge domain of topology shapes with composites is more reasonable than that with isotropic materials.Consequentially,single-point connection is avoided and deformation capability is increased by 2.1 times.In the same conditions,better deformation and bearing capability are achieved by adjusting the fiber orientations.(2)Topology design and analysis of compliant mechanisms with variable stiffness composites laminated plates.Mathematical description of curved fiber paths in variable laminated plates are model using the shifting method and an equivalent constitutive relation is built.Based on the classical penalized models,topology optimization method of compliant mechanisms with variable stiffness laminated plates is proposed.Compliant inverters and grippers are taken as numerical examples to design topology shapes and compare with constant stiffness laminated plates.The results show that the ability to deform of compliant mechanisms is increased by22.5%,7% respectively and the stress levels are reduced by 8%,12% respectively.In the same conditions,stress characteristics in hinge domain can be changed by adjusting the fiber paths.Therefore,it is obvious that deformation capability is increased and stress level is reduced in compliant mechanisms.Moreover,the advantages of compliant mechanisms are also reflected by using variable stiffness composite laminated plates.(3)Optimization method of combining fiber orientations and topology shapes for constant stiffness composites laminated plates.Focusing on the non-convex question derived from direct optimization of fiber angles,optimization model of combining fiber orientations and topology shapes for mechanisms or structures with constant stiffness laminated plates,in which deformation and bearing capability are viewed as optimization objective,is obtained.Lamination parameters and relative density are taken as design variables to decide the fiber orientations and materials distribution in the model.Based on the MMA method,a multi-step solving method for combined optimization is proposed.Then,optimum design of combining topology shapes and fiber orientations are investigated via cantilever beam and compliant inverters design examples.Finally,validities of the results obtained by the proposed method are analyzed and verified by exhaustive method.The results show that optimum fiber orientations and topology shapes for compliant mechanisms and structures can be obtained simultaneously using the proposed method.Moreover,the method has higher optimization efficiency.Compared with balanced symmetric laminated plates,deformation and bearing capability of cantilever beam and compliant inverters with symmetric laminated plates are increased by 6.5% and 4.2% respectively in the same conditions.The method combines composites optimization and topology optimization and lays the basis of optimum design of compliant mechanisms and structures with constant stiffness laminated plates.(4)Optimization method of combining fiber paths and topology shapes for variable stiffness composites laminated plates.Optimization model of combining fiber paths and topology shapes for mechanisms or structures with variable stiffness laminated plates,in which nodal lamination parameters and relative density are viewed as design objective,is obtained based on the shape function interpolation method.Firstly,optimum topology shapes and nodal laminated parameters are obtained by non-monotonic GCMMA method.Then,under the curvature constraint,matching of nodal lamination parameters and fiber orientations is achieved by the least square method.Finally,discrete nodal fiber orientations are fitted to continuous fiber paths by virtue of concept of the streamline and features of the stream function.Combining optimum design is investigated via cantilever beam and compliant inverters design examples.Compared with the combining optimization method for constant stiffness laminated plates,deformation and bearing capability are increased by 5.8% and 14% respectively in the same conditions.The results show that optimum fiber paths and topology shapes for compliant mechanisms and structures with variable stiffness laminated plates are obtained using the proposed method.Moreover,the proposed method provides the way to generate continuous fiber paths for the automatic fiber placement machines.(5)Topology design and experiment analysis of compliant wing leading-edge and trailing-edge with composites laminated plates.Based on the analysis of flight performance,the least squares between the actual deformation and desired shape are taken as the optimization objective.Then,optimum mechanism design of compliant leading-edge and trailing-edge is achieved using the optimum method of combining fiber orientations and topology shapes for constant stiffness laminated plates.Moreover,deformation capability of compliant leading-edge and trailing-edge is also experiment investigated.Effectiveness of deformation for compliant leading-edge and trailing-edge is discussed and verified.Therefore,the paper provides the technical support that composites are used to design compliant morphing wings in unmanned aerial vehicle.