Layout and material gradation in topology optimization of functionally graded structures: a global-local approach

By means of continuous topology optimization, this paper discusses the influence of material gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including material gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering material gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular materials.

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.

Impact on HDPE and PVC plates - Experimental tests and numerical simulations

This paper presents first material tests on HDPE and PVC, and subsequently impact tests on plates made of the same materials. Finally, numerical simulations of the plate impact tests are compared with the experimental results. A rather comprehensive series of mechanical material tests were performed to disclose the behaviour of PVC and HDPE in tension and compression. Quasi-static tests were carried out at three rates in compression and two in tension. Digital image correlation. DIC, was used to measure the in-plane strains, revealing true stress-strain curves and allowing to analyze strain-rate sensitivity and isotropy of Poisson`s ratio. In addition, dynamic compression tests were carried out in a split-Hopkinson pressure bar. Quasi-static and dynamic tests were also performed on clamped plates made of the same PVC and HDPE materials, using an optical technique to measure the full-field out-of-plane deformations. These tests, together with the material data, were used for comparative purposes of a finite element analysis. A reasonable agreement between experimental and numerical results was achieved. (C) 2010 Elsevier Ltd. All rights reserved.

An experimental and numerical investigation on tyre impact

A key issue in the design of tyres is their capability to sustain intense impact loads. Hence, the development of a reliable experimental data basis is important, against which numerical models can be compared. Experimental data on tyre impact in the open literature is somewhat rare. In this article, a specially design rig was developed for tyre impact tests. It holds the test piece in a given position, allowing a drop mass with a round indenter to hit pressurised tyres with different impact energies. A high-speed camera and a laser velocimeter were used to track the impact event. From the laser measurement it was possible to obtain the impact force and the local indentation. A finite element study was then conducted using material properties from the open literature. By comparing the experimental measurements with the numerical results, it became evident that the model was capable of predicting the major features of the impact of a mass on a tyre. This model is therefore of value for the assessment of the performance of a tyre in extreme cases of mass impact. (C) 2009 Elsevier Ltd. All rights reserved.

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.

Modeling of functionally graded piezoelectric ultrasonic transducers

The application of functionally graded material (FGM) concept to piezoelectric transducers allows the design of composite transducers without interfaces, due to the continuous change of property values. Thus, large improvements can be achieved, as reduction of stress concentration, increasing of bonding strength, and bandwidth. This work proposes to design and to model FGM piezoelectric transducers and to compare their performance with non-FGM ones. Analytical and finite element (FE) modeling of FGM piezoelectric transducers radiating a plane pressure wave in fluid medium are developed and their results are compared. The ANSYS software is used for the FE modeling. The analytical model is based on FGM-equivalent acoustic transmission-line model, which is implemented using MATLAB software. Two cases are considered: (i) the transducer emits a pressure wave in water and it is composed of a graded piezoceramic disk, and backing and matching layers made of homogeneous materials; (ii) the transducer has no backing and matching layer; in this case, no external load is simulated. Time and frequency pressure responses are obtained through a transient analysis. The material properties are graded along thickness direction. Linear and exponential gradation functions are implemented to illustrate the influence of gradation on the transducer pressure response, electrical impedance, and resonance frequencies. (C) 2009 Elsevier B. V. All rights reserved.

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

Embrittlement of case hardened steel chain link

Various steel chain links presented cracking during their manufacturing process, which includes induction case hardening and electrogalvanizing steps. Fractographic examination of the exposed crack surfaces revealed intergranular cracking with some areas featuring a thin layer of iron oxide, indicating that the cracking took place after the electrogalvanizing step. The location of the cracks coincided with the position of the deepest case hardened layer, suggesting the occurrence of localized overheating during the induction case hardening step. Inductive heating finite element analysis (COSMOS Designstar Software) confirmed that during the case hardening the austenitising temperature reached in the crack region values of approximately 1050 degrees C. The results indicated that intergranular cracking was caused by hydrogen embrittlement. (C) 2009 Elsevier Ltd. All rights reserved.

Numerical modeling of ductile crack extension in high pressure pipelines with longitudinal flaws

This study examines the applicability of a micromechanics approach based upon the computational cell methodology incorporating the Gurson-Tvergaard (GT) model and the CTOA criterion to describe ductile crack extension of longitudinal crack-like defects in high pressure pipeline steels. A central focus is to gain additional insight into the effectiveness and limitations of both approaches to describe crack growth response and to predict the burst pressure for the tested cracked pipes. A verification study conducted on burst testing of large-diameter, precracked pipe specimens with varying crack depth to thickness ratio (a/t) shows the potential predictive capability of the cell approach even though both the CT model and the CTOA criterion appear to depend on defect geometry. Overall, the results presented here lend additional support for further developments in the cell methodology as a valid engineering tool for integrity assessments of pipelines with axial defects. (C) 2011 Elsevier Ltd. All rights reserved,

Understanding Contradictory Data in Contraction Stress Tests

The literature shows contradictory results regarding the role of composite shrinkage and elastic modulus as determinants of polymerization stress. The present study aimed at a better understanding of the test mechanics that could explain such divergences among studies. The hypothesis was that the effects of composite shrinkage and elastic modulus on stress depend upon the compliance of the testing system. A commonly used test apparatus was simulated by finite element analysis, with different compliance levels defined by the bonding substrate (steel, glass, composite, or acrylic). Composites with moduli between 1 and 12 GPa and shrinkage values between 0.5% and 6% were modeled. Shrinkage was simulated by thermal analogy. The hypothesis was confirmed. When shrinkage and modulus increased simultaneously, stress increased regardless of the substrate. However, if shrinkage and modulus were inversely related, their magnitudes and interaction with rod material determined the stress response.

Measuring Bond Strength Between Fiber Post and Root Dentin: A Comparison of Different Tests

Purpose The aim of this study was to evaluate the ability of bond strength tests to accurately measure the bond strength of fiber posts luted into root canals Materials and Methods The test methods studied were hourglass microtensile (HM), push-out (PS), modified push out (MP) and pull out (PL) The evaluated parameters were bond strength values, reliability (using Weibull analysis), failure mode (using confocal microscopy), and stress distribution (using finite element analysis) Forty human intact single rooted and endodontically treated teeth were divided into four groups Each group was assigned one of the test methods The samples in the HM and PS groups were 1 0 +/- 0 1 mm thick, the HM samples were hourglass shaped and the PS samples were disk shaped For the PL and MP groups, each 1 mm dentin slice was luted with a fiber post piece Three dimensional models of each group were made and stress was analyzed based on Von Mises criteria Results PL provided the highest values of bond strength followed by MP both of which also had greater amounts of adhesive failures PS showed the highest frequency of cohesive failures MP showed a more homogeneous stress distribution and a higher Weibull modulus Conclusion The specimen design directly influences the biomechanical behavior of bond strength tests

Can Fiber Posts Increase Root Stresses and Reduce Fracture?

The clinical success of fiber posts has been attributed to their lower elastic modulus. The tested hypothesis was that fiber posts could lead to lower risk of post debonding and lower risk of root fracture, despite an increase in root stresses. Stress analyses were carried out with a 3D finite element model of a premolar restored with a metallic or a fiber post. Bonded and non-bonded post/cement interface conditions were simulated. We calculated risk-of-fracture indices by determining the highest principal stress values divided by the tensile strength. Shear stresses along the post/cement interface were analyzed for the bonded models. Compared with the premolar restored with a metallic post, the fiber post generated lower stresses along the interface and higher stresses in the root. However, with the fiber post, fracture was less likely to occur in the root, since its core and post fracture indices were higher.

Direct comparison of the bond strength results of the different test methods: A critical literature review

Objective. The goal of this paper is to undertake a literature search collecting all dentin bond strength data obtained for six adhesives with four tests ( shear, microshear, tensile and microtensile) and to critically analyze the results with respect to average bond strength, coefficient of variation, mode of failure and product ranking. Method. A PubMed search was carried out for the years between 1998 and 2009 identifying publications on bond strength measurements of resin composite to dentin using four tests: shear, tensile, microshear and microtensile. The six adhesive resins were selected covering three step systems ( OptiBond FL, Scotch Bond Multi-Purpose Plus), two-step (Prime & Bond NT, Single Bond, Clear. l SE Bond) and one step (Adper Prompt L Pop). Results. Pooling results from 147 references showed an ongoing high scatter in the bond strength data regardless which adhesive and which bond test was used. Coefficients of variation remained high (20-50%) even with the microbond test. The reported modes of failure for all tests still included high number of cohesive failures. The ranking seemed to be dependant on the test used. Significance. The scatter in dentin bond strength data remains regardless which test is used confirming Finite Element Analysis predicting non-uniform stress distributions due to a number of geometrical, loading, material properties and specimens preparation variables. This reopens the question whether, an interfacial fracture mechanics approach to analyze the dentin - adhesive bond is not more appropriate for obtaining better agreement among dentin bond related papers. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Elastic modulus of posts and the risk of root fracture

The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts` elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (sigma(max)) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (processing). Load of 100 N was applied, varying the directions (0 degrees, 45 degrees and 90 degrees) in relation to the post`s long axis. The magnitude and direction of the sigma(max) were recorded. At the 45 degrees and 90 degrees loading, the highest values of sigma(max) were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0 degrees loading, the highest values of sigma(max) were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the sigma(max) generated on the root was dependent on the loading direction.

Effect of cantilever length and framework alloy on the stress distribution of mandibular-cantilevered implant-supported prostheses

The purpose of this in vitro study was to analyze the stress distribution on components of a mandibular-cantilevered implant-supported prosthesis with frameworks cast in cobalt-chromium (Co-Cr) or palladium-silver (Pd-Ag) alloys, according to the cantilever length. Frameworks were fabricated on (Co-Cr) and (Pd-Ag) alloys and screwed into standard abutments positioned on a master-cast containing five implant replicas. Two linear strain gauges were fixed on the mesial and distal aspects of each abutment to capture deformation. A vertical static load of 100 N was applied to the cantilever arm at the distances of 10, 15, and 20 mm from the center of the distal abutment and the absolute values of specific deformation were recorded. Different patterns of abutment deformation were observed according to the framework alloy. The Co-Cr alloy framework resulted in higher levels of abutment deformation than the silver-palladium alloy framework. Abutment deformation was higher with longer cantilever extensions. Physical properties of the alloys used for framework interfere with abutment deformations patterns. Excessively long cantilever extensions must be avoided. To cite this article:Jacques LB, Moura MS, Suedam V, Souza EAC, Rubo JH. Effect of cantilever length and framework alloy on the stress distribution of mandibular-cantilevered implant-supported prostheses.Clin. Oral Impl. Res. 20, 2009; 737-741.doi: 10.1111/j.1600-0501.2009.01712.x.