【作者】 王睿；

【导师】 亢战；

【作者基本信息】 大连理工大学 ， 工程力学， 2017， 博士

【摘要】 与传统的单一常规材料结构相比,双材料结构可具有更好的作动、减振等特殊性能,能够实现某些特定的工程需求。其中,压电-常规材料和阻尼-常规材料就是较为常见的双材料结构。集成压电作动器的结构被广泛应用于高精度作动、微型阀、微型泵、空气动力学流动控制和主动形状控制等工程领域,因此需要研究内嵌压电作动器结构材料最优分布问题以获得更好的结构作动性能。阻尼-常规材料结构更多的应用于振动控制领域,阻尼材料的布局对于结构的减振效果有显著影响。本文针对双材料结构构型优化设计问题复杂的特点,基于有限元方法,以连续体结构拓扑优化设计方法作为基础研究了双材料作动与减振结构的拓扑优化问题。主要的研究内容分为以下三个部分:1.内嵌压电作动器的结构构型与控制电压集成优化方法。主要研究了以最大化指定点的输出位移为目标的结构常规材料和压电材料的同时分布问题,通过幂律惩罚的两相材料模型描述作动压电材料单元和周围耦合单元。为了实现最优的作动性能,在考虑常规材料和压电材料密度分布的同时将作动控制电压作为设计变量引入到拓扑优化设计当中,构造了三值化作动电压的特定插值模型。基于外加电压和参数化设计变量之间的插值惩罚,将三值化的离散电压优化问题转化成为一个连续的优化问题。基于伴随变量法给出了目标函数的灵敏度分析。数值算例表明,引入电压设计变量后,结构的作动性能得到很好的提升,可以实现更大的输出位移。2.敷设阻尼材料的减振结构阻尼材料层拓扑优化方法。优化问题中的设计目标是在给定阻尼材料用量的情况下最小化结构的动柔度,以阻尼材料的相对密度作为设计变量。采用类似于SIMP模型的人工阻尼惩罚模型,该模型可惩罚阻尼材料的中间密度,以便能获得更为清晰的拓扑构型。由于结构呈现非比例阻尼特性,因此使用基于降阶技术的状态空间下的复模态叠加法来计算结构的稳态响应和动柔度。采用了伴随变量法对动柔度进行灵敏度分析。数值算例讨论了阻尼系数和外加载荷频率等主要参数对拓扑优化结果的影响。在单一外加载荷频率优化问题的基础上将外加载荷频率推广到某一频率区间,由于目标函数变为离散函数,因此通过引入凝聚函数对所选取频率区间内的动柔度进行包络,将离散的原优化问题转化为连续可微的新优化问题,数值算例验证了引入凝聚函数后优化模型的有效性。3.考虑瞬态响应的薄壁结构阻尼材料层的拓扑优化设计。主要研究了以最小化阻尼减振结构瞬态动力学响应为目标的阻尼材料层最优分布问题。基于SIMP方法构造人工阻尼材料惩罚模型和结构拓扑优化模型,以阻尼材料的相对密度作为设计变量,给定阻尼材料用量为约束条件,优化问题的目标函数为给定位置的瞬态位移响应平方的时间积分。由于阻尼材料层在优化的过程中为局部分布的拓扑形式,结构整体呈现非比例阻尼特性,采用逐步积分法对结构的振动方程进行求解。通过伴随变量法给出了一般形式下目标函数对设计变量的灵敏度表达式,在此基础上采用基于梯度的移动渐近线方法求解,得到了与考虑稳态响应的优化问题不同的拓扑优化结果。数值算例验证了优化模型与算法的合理性和有效性,讨论了体积分数、时间区间以及载荷形式等参数的改变对优化结果的影响。更多还原

【Abstract】 Compared with traditional single conventional material structures,bi-material structures have better special performance in some engineering requirements,such as actuation and vibration suppression.Therein,the two common bi-material structures are piezoelectric-conventional material structure and damping-conventional material structure.Piezoelectric actuator-integrated structures are suitable for a wide range of applications such as high precision actuation,microvalve,micropump,aerodynamic flow control and active shape control.Therefore,it is necessary to research the topology optimization of bi-material structure with embedded in-plane piezoelectric actuators.The layout of damping material has significant effect for reducing the vibration of structures,so damping-conventional material structures are usually employed to control the structural vibration.The topology optimization design problems of bi-material structures optimization are complex.Based on the finite element method and topology optimization design methods of continuum structures,the structural topology optimization problems of bi-material for actuation and vibration suppression are investigated in this thesis.The main research contents are introduced as follows:1.Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation.This dissertation investigates the topology optimization of conventional material and piezoelectric material structural layout with embedded in-plane piezoelectric actuators.The maximization of the nodal displacement at a selected output port is considered as the design objective.A two-phase material model with power-law penalization is employed in the topology optimization of the actuator elements and the coupled surrounding structure.In order to incorporate the actuation voltage directly into the design for achieving the best overall actuation performance,element-wise voltage design variables are also included in the optimization.A special interpolation scheme between the tri-level voltage values and the design variables is used in the optimization model.Therein,the tri-level discrete voltage optimization is converted into a continuous optimization based on a penalized interpolation between the applied voltage and the parametric design variables.The adjoint variable method for the sensitivity analysis of objective function is derived.Numerical examples confirmed that the actuation performance is improved and larger output displacement can be achieved by introducing voltage design variables into the design problem.2.The topology optimization method of damping layer for reducing the structural vibration with damping materials.The design objective of optimization problem is minimizing the dynamic compliance of the structure under a given volume constraint of the damping material and the relative densities of damping material are taken as design variables.Therein,an artificial damping material model that has a similar form as in the SIMP approach is suggested and the intermediate density of the damping material is penalized in order to acquire a clear topology distribution.Since the damping structure is non-proportional,the steady-state response and dynamic compliance of the vibrating structure are calculated by using the complex mode superposition method based on model reduction technique in the state space.The analysis of the dynamic compliance sensitivity is implemented by using the adjoint variable method.The influences of main parameters such as damping coefficients and excitation frequencies are discussed on topology optimization results in numerical examples.Based on the solution of optimization problem under a single load frequency,the excitation frequency is extended to a certain frequency range.Since the objective function becomes discrete,the aggregate function is employed to form an envelope function,and the original discrete problem is converted into a new optimization problem with continuous and differentiable.Numerical examples are presented to demonstrate the validity of the optimal model by introducing the aggregate function.3.Topology optimization design of damping layer in thin-plate structures considering transient response.The optimal distribution of damping material is investigated and the design objective is to minimize the transient response of the vibrating structures.Based on the SIMP method,the artificial damping penalty model and topology optimization model are adopted.Therein,the relative densities of the damping material are taken as design variables and the volume constraint of damping material is considered.The objective function is the time integration of the structural transient response at specified positions.Since the structure exhibits a non-proportional damping effect,the structural vibration equation is solved by using the time integration method.The design sensitivities of the vibrating structure under applied loads are calculated by using the adjoint variable method.Then the topology optimization problem is solved with the method of moving asymptote algorithm,which is a gradient-based method.The optimal results are different from the results of structural optimization considering steady-state response.Numerical examples are presented for demonstrating the validity and effectiveness of the proposed optimization model and numerical techniques.The influences of variations in parameters such as volume fraction,time interval and load form on the results of optimization problem are discussed.更多还原