Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental onesCNPqFAPES

Design of piezocomposite materials and piezoelectric transducers using topology optimization.

Piezoelectric materials are widely used in electromechanical sensors and actuators, in electronic equipment as resonators, and in acoustic applications as ultrasonic transducers and hydrophones for generating and detecting sound waves. Their development has been based on the use of simple analytical models, test of prototypes, and analysis by the finite element method (FEM), usually limiting their design to a parametric optimization. By changing the topology of these devices or their components, we may obtain new kinds of piezocomposites and transducers with better performance characteristics. This dissertation describes the application of topology optimization combined with the homogenization method and FEM for designing piezocomposite materials and piezoelectric transducers. The optimized solution is obtained using Sequential Linear Programming. Three problems are discussed: design of piezocomposite materials, design of resonators and ultrasonic transducers, and design of piezoelectric actuators. The performance characteristics of piezocomposite materials can be improved by designing new topologies of microstructures (or unit cells) for these materials. The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite. By changing the unit cell topology, performance characteristics can be vastly improved in the piezocomposite. Hydrophone (low-frequency) and ultrasonic transducer (high-frequency) applications are considered. A general homogenization method applied to piezoelectricity was implemented using FEM to calculate the effective properties of a unit cell with complex topology. This method has no limitations regarding volume fraction or shape of the composite constituents. The main assumption is the periodicity of the unit cell. The performance characteristics are improved by orders of magnitude comparing with common configurations of piezocomposite unit cells, as confirmed by results of experiments conducted with manufactured prototypes of some optimized piezocomposites. In the design of resonators and ultrasonic transducers, three kinds of objectives are specified: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies; and design a transducer with narrow-band or broadband response. The results show new transducer configurations with better performance. In the design of piezoelectric actuators, we focus on the low-frequency flextensional actuators which consist of a piezoceramic connected to a coupling structure that converts and amplifies the piezoceramic output displacement. By designing new kinds of coupling structure, flextensional actuators for different tasks can be obtained. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common configurations.Ph.D.Applied SciencesElectrical engineeringMaterials scienceMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131327/2/9840648.pd

Vibrational modeling of piezoelectric ultrasonic transducers by the finite element method.

Apresentam-se as bases teóricas do Método de Elementos Finitos (MEF) piezoelétrico, e a sua aplicação na modelagem de transdutores de ultra-som piezoelétricos, que consiste na determinação das características vibracionais (frequências de ressonância e anti-ressonância, modos de vibrar e coeficiente de acoplamento eletromecânico), obtenção da curva de admitancia, análise transiente da estrutura piezoelétrica sujeita a uma excitação pulsada e análise da influência da variação das constantes piezoelétricas do transdutor com o raio. Utilizando-se o MEF aplicado a acústica obteve-se o campo acústico gerado pelo transdutor operando em onda contínua, bem como iniciou-se o estudo da propagação de ondas num líquido, analisando-se as ondas geradas pela excitação pulsada de um pistão plano em contato com o fluido. Os modos de vibrar e os valores de frequências de ressonância obtidos para um transdutor, foram comparados com os resultados experimentais.The theoretical basis of piezoelectric finite element method (FEM), and its application in piezoelectric ultrasonic transducer modelling is presented. Among these applications we have the calculation of resonance and antiresonance frequencies, vibration modes, piezoelectric coupling coefficient, admittance curve and transient analysis of piezoelectric structure excited by a short pulse. By means of piezoelectric FEM the influence of variation of piezoelectric constant with radius is analysed. It is discussed three kind of functions (linear, cosinoidal and Gaussian). This technique is called apodization. The acoustic filed generated by the transducer operating in continuous wave (CW) was calculated by using FEM applied to acoustic, considering the fluid-structure coupling. The study of wave propagation in liquids is started by using FEM, analyzing the waves generated by a plane piston in contact with the fluid, excited by a short pulse. For each case discussed above, all boundary conditions and hypothesis assumed in the construction of finite element models are discussed. Although the models considered are circular transducers, the concepts acquired can be expanded to other geometries. The vibrational modes were visualized by means of a laser interferometry technique (ESPI), and the admittance curves were measured by using an impedometer. These results were compared with the FEM results, and the models precision was discussed

Vibrational modeling of piezoelectric ultrasonic transducers by the finite element method.

Apresentam-se as bases teóricas do Método de Elementos Finitos (MEF) piezoelétrico, e a sua aplicação na modelagem de transdutores de ultra-som piezoelétricos, que consiste na determinação das características vibracionais (frequências de ressonância e anti-ressonância, modos de vibrar e coeficiente de acoplamento eletromecânico), obtenção da curva de admitancia, análise transiente da estrutura piezoelétrica sujeita a uma excitação pulsada e análise da influência da variação das constantes piezoelétricas do transdutor com o raio. Utilizando-se o MEF aplicado a acústica obteve-se o campo acústico gerado pelo transdutor operando em onda contínua, bem como iniciou-se o estudo da propagação de ondas num líquido, analisando-se as ondas geradas pela excitação pulsada de um pistão plano em contato com o fluido. Os modos de vibrar e os valores de frequências de ressonância obtidos para um transdutor, foram comparados com os resultados experimentais.The theoretical basis of piezoelectric finite element method (FEM), and its application in piezoelectric ultrasonic transducer modelling is presented. Among these applications we have the calculation of resonance and antiresonance frequencies, vibration modes, piezoelectric coupling coefficient, admittance curve and transient analysis of piezoelectric structure excited by a short pulse. By means of piezoelectric FEM the influence of variation of piezoelectric constant with radius is analysed. It is discussed three kind of functions (linear, cosinoidal and Gaussian). This technique is called apodization. The acoustic filed generated by the transducer operating in continuous wave (CW) was calculated by using FEM applied to acoustic, considering the fluid-structure coupling. The study of wave propagation in liquids is started by using FEM, analyzing the waves generated by a plane piston in contact with the fluid, excited by a short pulse. For each case discussed above, all boundary conditions and hypothesis assumed in the construction of finite element models are discussed. Although the models considered are circular transducers, the concepts acquired can be expanded to other geometries. The vibrational modes were visualized by means of a laser interferometry technique (ESPI), and the admittance curves were measured by using an impedometer. These results were compared with the FEM results, and the models precision was discussed

Topology Optimization Design Of Functionally Graded Structures

Functionally Graded Materials (FGMs) possess continuously graded material properties and are characterized by spatially varying microstructures. Such materials are studied in conjunction with the concept of topology optimization design which determines holes and connectivities of the structure by adding and removing material in the extended fixed design domain. The objective is to design FGM structures by using the concept of continuum topology optimization which considers a continuum distribution of the design variable inside the finite element domain. The traditional formulation for stiffness design problem is considered where the objective is to find the material distribution that minimizes the mean compliance. Two distinct, but related, applications are considered. The first application considers the objective of designing a structure in an FGM domain where the properties change in a certain direction according to a specified law, which leads to a structure with asymmetric stiffness properties. A new material model, called FGM-SIMP (Functionally Graded Material -- Solid Isotropic Material with Penalization), is defined based on the traditional SIMP model. The second application consists of finding the optimal material gradation law inside the design domain. In this case we expect to obtain intermediate material properties inside the design domain. A material model obeying the Hashin-Strikman bounds is applied. Because current FGM manufacturing techniques emphasize layered systems, a layered material constraint is adopted. Different from the traditional topology optimization problem which focuses on a 0-1 design, we seek intermediate properties at the end of the optimization process. The optimality criteria method is applied to solve the optimization problem. The alg..

Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo State Research Support Foundation, Sao Paulo, Brazil)[06/50640-2]FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo State Research Support Foundation, Sao Paulo, Brazil)[06/57805-7]CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, National Council of Scientific and Technological Development, Brazil)[303689/2009-9

Design of compliant mechanisms considering thermal effect compensation and topology optimization

Compliant mechanisms can achieve a specified motion as a mechanism without relying on the use of joints and pins. They have broad application in precision mechanical devices and Micro-Electro Mechanical Systems (MEMS) but may lose accuracy and produce undesirable displacements when subjected to temperature changes. These undesirable effects can be reduced by using sensors in combination with control techniques and/or by applying special design techniques to reduce such undesirable effects at the design stage, a process generally termed ""design for precision"". This paper describes a design for precision method based on a topology optimization method (TOM) for compliant mechanisms that includes thermal compensation features. The optimization problem emphasizes actuator accuracy and it is formulated to yield optimal compliant mechanism configurations that maximize the desired output displacement when a force is applied, while minimizing undesirable thermal effects. To demonstrate the effectiveness of the method, two-dimensional compliant mechanisms are designed considering thermal compensation, and their performance is compared with compliant mechanisms designs that do not consider thermal compensation. (C) 2010 Elsevier B.V. All rights reserved.FAPESP-Sao Paulo State Foundation Research AgencyFAPESP[2006/57805-7]CNPq-National Council for Scientific and Technological Development[303689/2009-9

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.FUSP (Fundacao de Apoio a Universidade de Sao Paulo)FUSP (Fundacao de Apoio a Universidade de Sao Paulo) [182208]CNPq (National Council for Research and Development, Brazil)CNPq (National Council for Research and Development, Brazil) [303689/2009-9]Sao Paulo Research Foundation (FAPESP)FAPESP (Sao Paulo Research Foundation) [2011/02387-4]Air Force Office of Scientific ResearchAir Force Office of Scientific Research [FA9550-09-1-0686

Integral Piezoactuator System with Optimum Placement of Functionally Graded Material - A Topology Optimization Paradigm

Piezoactuators consist of compliant mechanisms actuated by two or more piezoceramic devices. During the assembling process, such flexible structures are usually bonded to the piezoceramics. The thin bonding layer(s) between the compliant mechanism and the piezoceramic may induce undesirable behavior, including unusual interfacial nonlinearities. This constitutes a drawback of piezoelectric actuators and, in some applications, such as those associated to vibration control and structural health monitoring (e. g., aircraft industry), their use may become either unfeasible or at least limited. A possible solution to this standing problem can be achieved through the functionally graded material concept and consists of developing `integral piezoactuators`, that is those with no bonding layer(s) and whose performance can be improved by tailoring their structural topology and material gradation. Thus, a topology optimization formulation is developed, which allows simultaneous distribution of void and functionally graded piezoelectric materials (including both piezo and non-piezoelectric materials) in the design domain in order to achieve certain specified actuation movements. Two concurrent design problems are considered, that is the optimum design of the piezoceramic property gradation, and the design of the functionally graded structural topology. Two-dimensional piezoactuator designs are investigated because the applications of interest consist of planar devices. Moreover, material gradation is considered in only one direction in order to account for manufacturability issues. To broaden the range of such devices in the field of smart structures, the design of integral Moonie-type functionally graded piezoactuators is provided according to specified performance requirements.FUSP (University of Sao Paulo Foundation)Polytechnic School of University of Sao Paulo (USP, Brazil)[08/51070 - 0]FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo)CNPq[s 303689/2009-9]University of Illinois at Urbana-Champaign (UIUC

Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems

This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; however, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the `modal assurance criterion` is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear programming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.FAPESP (Sao Paulo State Foundation Research Agency)[05/01762-5]FAPESP (Sao Paulo State Foundation Research Agency)[2006/57805-7]FAPESP (Sao Paulo State Foundation Research Agency)[2008/5070-0]CNPq - National Council for Research and Development, Brazil[304208/2006-0