We propose a strongly coupled partitioned iterative method for directly solving coupled elastic body and piezoelectric continuum (Class I) and hierarchically coupled inverse and direct-piezoelectric effects (Class II) in piezo-actuated compliant mechanisms (triply coupled problem). The proposed method combines the Dirichlet-Neumann partitioned procedure with the force and displacement relaxations and the block Gauss-Seidel procedure based on the hierarchical decomposition of the triply coupled problem. The convergence properties are theoretically derived from a linear spring model, and the procedures of the proposed method are theoretically analyzed using block iterative interpretations on linear monolithic coupled problems, leading to their comprehensive understanding. In particular, the force relaxation shows the better convergence for the triply coupled problem due to incomplete under-relaxation. The theoretical results are verified, and the validity of the proposed method is demonstrated numerically and experimentally.

This paper proposes 2.5-dimensional polymer micromachined insect-mimetic wings based on a fluid-structure interaction (FSI) design concept that enables natural deformations like cambering and pitching under fluid forces. Instead of directly employing an analysis for the FSI, an iterative structural Design Window (DW) search is used to reduce the computational cost significantly. A DW search using the iterative method refines the initial design by addressing fabrication challenges and tuning it to meet manufacturability constraints. The successful fabrication and demonstration of the final design solution for a wing demonstrates the effectiveness of the iterative DW search based on the FSI design concept. Furthermore, a pixel model is introduced to convert an unstructured to a structured mesh for the FSI analysis to further reduce the computational cost. The camber and pitching error between the unstructured and structured meshes is minimized to achieve insect-like aerodynamic performance by adjusting the elastic moduli of center and root veins. Finally, an analysis for the FSI is conducted, based on the parameters obtained from the pixel model to evaluate the flight performance on the basis of the lift, camber, and pitching required by an actual insect to maneuver and hover.

In this study, we propose a 2.5-dimensional (2.5-D) structure approach for insect-mimetic flapping-wing air vehicles (FWAVs). The proposed approach includes design and fabrication methods. To our best knowledge, this study is the first one that develops a flapping system for FWAVs without any post-assembly of structural components. The proposed structure consists of a transmission, a supporting frame, and elastic wings. The transmission transforms the small translational displacement produced by a piezoelectric bimorph into a large rotational displacement of the wings. The size is reduced using the proposed design method. Then, the 2.5-D structure is fabricated using the proposed polymer MEMS micromachining method. The presented micro flapping system flaps the wing with a stroke angle and flapping frequency comparable to those of actual small insects using resonance. The results confirm that the proposed approach can miniaturize FWAVs.

In flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi-implicit scheme for monolithic fluid-structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid-to-fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node-positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid-to-fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings. We developed a novel computational framework that consists of a fully parallelized solution method using algebraic splitting and semi-implicit scheme for monolithic FSI equation systems, the parallel CG method, and a pixel model wing combined with explicit node-positioning.Using the proposed framework, we found that feathering and cambering motions in flapping insect wings will be given based on the equilibrium between wing's elastic and aerodynamic forces, and these motions are enhanced by the wing's inertial force.image

Multilayered flexible piezoelectric energy harvesting devices (FPEDs) are a new future harvesting technology which are highly flexible and lightweight than familiar cantilever piezoelectric energy harvesters. This mechanical vibration driven FPED is a strongly coupled multiphysics phenomena that involve complex natural three-way interaction among the composite piezoelectric structure, the electric charge accumulated in the piezoelectric material, and a controlling electrical circuit attached to it. Efficient and accurate computational solution approaches are essential for analyzing these mechanical vibration-driven FPEDs to capture the main physical aspect of the coupled phenomena and to accurately predict the output voltage. While there are some numerical models for simple familiar cantilever type piezoelectric energy harvester reported in the literature, a fully three-dimensional strongly coupled model for complex material distributed, complex geometry, and multilayered FPED involving strong coupling of structure, piezoelectricity, and circuit phenomena has not yet been developed. A partitioned iterative algorithm is developed using a hierarchical decomposition approach wherein the coupled three fields are solved separately and coupled through loop union integration techniques that provide an efficient and accurate simulation of FPEDs. The simulation results matched the experiment results very well. This study provides a basis for the natural extension of partitioned iterative finite element coupled algorithm to simulate the future piezoelectric energy harvesting technologies involving a strong coupling of structure, piezoelectricity, and circuit phenomenon.

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters. Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations. Each formulation has its advantages and disadvantages, and the choice depends on the characteristics of each coupled problem. This study proposes a new option: a coupled analysis strategy that combines the best features of the existing formulations, namely, the hybrid partitioned -monolithic method. The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm. In a typical benchmark problem of a piezoelectric energy harvester, this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method, discussing the accuracy, stability, and computational cost. The proposed hybrid concept is effective for coupled multi -physics problems, including various coupling conditions.

In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis of structure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectric coupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulations are used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely (1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weakly coupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially strongly coupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation for the two types of coupling, respectively. Numerical examples using a piezoelectric energy harvester, which is a typical structure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most cost-effective algorithm.

In this study, we propose a new feedback control model for insect flight maneuverability, and conduct the numerical analysis using the proposed model. In the proposed model, the feedback control based on the observation for actual insects is introduced to the partitioned analysis model for the wing-body interaction, where the flapping wings and the surrounding air flow coupling is monolithically formulated using a finite element method such that the wing's characteristic motions are simulated stably, while the one-way coupling from the wings to the body is used assuming a perturbation from the quasi -steady flight state. The roll control, on which we focus here, in our numerical result shows the good agreement with the body's attitude control of an actual insect observed in the previous experiment. In our future work, we will elucidate a maneuverability mechanism of controlling body's attitudes in insect flapping flight using the proposed model.

The flapping wings of insects undergo large deformations caused by aerodynamic forces, resulting in cambering. Insect-mimetic micro wings for flapping-wing nano air vehicles mimic these characteristic deformations. In this study, a 2.5-dimensional insect-mimetic micro wing model for flapping-wing nano air vehicles is proposed to realize this type of wing. The proposed model includes a wing membrane, a leading edge, a center vein, and a root vein, all of which are modeled as shell elements. The proposed wing is a 2.5-dimensional structure and can thus be fabricated using polymer micromachining. We conducted a design window search to demonstrate the capabilities of the wing. The design windows, which are areas of desirable design solutions in the design parameter space, are iteratively searched using nonlinear finite-element analysis under quasi-steady aerodynamic modeling. Here, thickness is selected as a design parameter. The properties of real insects, polymer materials, and fabrication conditions are used to determine the other parameters. A fabricable design solution that generates sufficient camber is found from the design windows.

This paper presents a novel fabricable design and demonstration of a polymer micromachined wing for flapping wing pico air vehicles, which is capable of producing camber deformations similar to those of real insects. The proposed wing is a 2.5-dimensional structure comprised of the leading edge, center, and root veins, and the wing membrane such that it can be fabricated using polymer micromachining. The design window that refers to the area of satisfactory design solutions is iteratively searched using a nonlinear finite element structural analysis. In the design problem, the mean camber is the design characteristic, the thickness of each vein is the design parameter, and the design constraint is the fabricability. A final design solution with sufficient camber is selected from the design window, and the fabricability is demonstrated using polymer micromachining.

It is still unclear how elastic deformation of flapping insect wings caused by the aerodynamic pressure results in their significant cambering. In this study, we present that a vein–membrane interaction (VMI) can clarify this mechanical process. In order to investigate the VMI, we propose a numerical method that consists of (a) a shape simplification model wing that consists of a few beams and a rectangular shell structure as the structural essence of flapping insect wings for the VMI, and (b) a monolithic solution procedure for strongly coupled beam and shell structures with large deformation and large rotation to analyze the shape simplification model wing. We incorporate data from actual insects into the proposed numerical method for the VMI. In the numerical analysis, we demonstrate that the model wing can generate a camber equivalent to that of the actual insects. Hence, the VMI will be a mechanical basis of the cambering of flapping insect wings. Furthermore, we present the mechanical roles of the veins in cambering. The intermediate veins increase the out-of-plane deflection of the wing membrane due to the aerodynamic pressure in the central area of the wing, while they decrease it in the vicinity of the trailing edge. As a result, these veins create the significant camber. The torsional flexibility of the leading-edge veins increases the magnitude of cambering.

Piezoelectric-structure interaction (PSI) and fluid-structure interaction (FSI) are multi-physics coupled systems. These interactions affect the vibration characteristics of coupled systems and thus such complex coupled systems must be controlled. This paper proposes computational control based on the finite element method for strongly coupled multi-physics analysis of the PSI of a thin flexible piezoelectric bimorph actuator. The vibration characteristics and the effect of direct velocity and displacement feedback (DVDFB) control in coupled systems are investigated. The displacement and velocity feedback gains are used together as well as separately. DVDFB control is extended to the FSI of stiff and soft structures to study vibration characteristics using active control and compare the stability of the two types of structure. The results of PSI show a reduction in actuator displacement amplitude and a shift in the resonance frequency due to DVDFB control. For FSI, the results for a stiff material show a reduction in displacement. The velocity feedback gain has no effect for a stiff material and leads to instability due to a large control force. The results for a soft material show a reduction in displacement and amplitude and more stability compared to the case for the stiff material.

In this study, an iterative design window (DW) search using nonlinear dynamic simulation was proposed for polymer micromachined flapping-wing nano air vehicles (FWNAVs) that can satisfy both nonlinear and unsteady design requirements, which are contradictory to each other. The DW is defined as an existing area of satisfactory solutions in the design parameter space. The present FWNAVs have a complete 2.5-dimensional structure such that they can be fabricated using polymer micromachining. The micro-wing of our FWNAVs has been designed using morphological and kinematic parameters of an actual dipteran insect. Finally, using our method, we found the DW that allowed miniaturization of the design down to 10 mm while satisfying all the design requirements. Our findings demonstrate the possibility of further miniaturizing FWNAVs down to the size of small flying insects.

In a micro piezoelectric drive system for insect-mimetic flapping wing nano air vehicles, a small translational displacement of the piezoelectric bimorph is converted to a large angular displacement using a transmission based on the geometric nonlinearity of large bending of the elastic hinges. The piezoelectric bimorph and the transmission strongly interact with each other due to the scale effect. Furthermore, in the piezoelectric bimorph, the direct and inverse piezoelectric effects are coupled with each other. Hence, in the micro piezoelectric drive system, the direct-piezoelectric, inverse-piezoelectric, and structural coupling occurs. In this study, a finite element analysis method based on the block successive under-relaxation method is proposed for the dynamic analysis of this triply coupled phenomena, and the dependency of the convergence property on the relaxation coefficient is investigated.

This paper demonstrates the importance of three-dimensional (3-D) piezoelectric coupling in the electromechan-ical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator. It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects (i.e., piezoelectric coupling effect). In addition, there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end (i.e., 3-D effect). Hence, modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices, which contributes to the accurate prediction of their behavior.

The novelty of this study includes the development of an insect-inspired flapping wing nano air vehicle (FWNAV) using polymer micromachining or MEMS flyer and its computational flight performance using a fluid-structure interaction (FSI) analysis. The present FWNAV consists of a micro transmission with a support frame, a micro wing, and a piezoelectric bimorph actuator. This FWNAV can be easily fabricated using polymer micromachining and its flight performance can be accurately predicted using the FSI analysis. Hence, this study will lead toward the development of tethered and flyable FWNAVs with the size of the smallest flying natural insects.

This study proposed a partitioned method with a feedback control to analyzed maneuvering of insects during flapping flight. This method decomposed the insect flapping flight into wing and body subsystems and then coupled them using feedback control. In the wing subsystem, the strong coupling of the flexible wings and surrounding fluid was accurately analyzed using the finite element method to obtain the thrust forces acting on the insect’s body. The resulting thrust forces were passed from the wing subsystem to the body subsystem, and then rigid body motion was analyzed in the body subsystem. The controlling of wing subsystem is done by the feedback control using the body angular displacement and velocity. The fundamental performance of the proposed method is demonstrated from the comparison between the present results and the actual observation of maneuver.

Insect flapping wings undergo large deformations such as feathering and cambering for creating large thrust forces. Hence, insect-mimetic wings for flapping wing nano air vehicles (FWNAVs) will replicate these characteristic deformations. For the purpose of realizing this type of wings, in this study, a 2.5-dimensional (2.5-D) insect-mimetic wing model for FWNAVs is proposed. The proposed wing model consists of the leading-edge, the central vein, the root vein, and the membrane, all of which are described by shell elements. The feathering and cambering of the proposed wing model can be caused by the aerodynamic pressure. Furthermore, the proposed wing can be fabricated using polymer micromachining because of the complete 2.5-D structure. In order to demonstrate these capabilities, we perform the design window (DW) search. The DW is defined as the existing area of satisfactory design solutions in the design parameter space, where each solution can produce a sufficient camber. The DWs for the leading-edge, the central and root veins are searched continuously using the geometrically nonlinear finite element analysis under quasi-steady aerodynamic modeling. The thickness is chosen as the design parameter, while the other parameters are set following actual insects and polymer materials. Finally, we determine the final solutions from the DWs for a specific polymer micromachining technique. In our future work, the proposed solutions will be manufactured for the future miniaturization of FWNAVs.