Topology Optimization Of Bi-material Structures For Actuation And Vibration Suppression

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.