M. Bodaghi

Self-expanding/shrinking structures by 4D printing

The aim of this paper is to create adaptive structures capable of self-expanding and self-shrinking by means of four-dimensional printing technology. An actuator unit is designed and fabricated directly by printing fibers of shape memory polymers (SMPs) in flexible beams with different arrangements. Experiments are conducted to determine thermo-mechanical material properties of the fabricated part revealing that the printing process introduced a strong anisotropy into the printed parts. The feasibility of the actuator unit with self-expanding and self-shrinking features is demonstrated experimentally. A phenomenological constitutive model together with analytical closed-form solutions are developed to replicate thermo-mechanical behaviors of SMPs. Governing equations of equilibrium are developed for printed structures based on the non-linear Green–Lagrange strain tensor and solved implementing a finite element method along with an iterative incremental Newton–Raphson scheme. The material-structural model is then applied to digitally design and print SMP adaptive lattices in planar and tubular shapes comprising a periodic arrangement of SMP actuator units that expand and then recover their original shape automatically. Numerical and experimental results reveal that the proposed planar lattice as meta-materials can be employed for plane actuators with self-expanding/shrinking features or as structural switches providing two different dynamic characteristics. It is also shown that the proposed tubular lattice with a self-expanding/shrinking mechanism can serve as tubular stents and grippers for bio-medical or piping applications.

Boundary element method applied to the bending analysis of thin functionally graded plates

The present work introduces the boundary element method applied to the bending analysis of functionally graded plates. It is assumed that material properties are graded through the thickness direction of the plate according to a power law distribution. The neutral surface position for such plate is determined and the classical plate theory based on the exact neutral surface position is employed to extract the equilibrium equations. A direct approach based on the Greens identity is used to formulate boundary element method. By introducing a novel approach, domain integrals which arise from distributed transverse loads are transformed into boundary integrals. In case studies, three geometrical shapes including, rectangular, circular and elliptic for functionally graded plates with/without hole are considered. Comparative studies are first carried out to evaluate the sufficiency of the proposed method for bending analysis of isotropic and functionally graded plates subjected to the transverse loads. Then, a series parametric study is performed to examine the influences of the power of functionally graded material, boundary conditions and geometrical parameters on the deformation and stress of functionally graded plates.

Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich beams resting on Pasternak foundation are presented. The carbon nanotubes (CNTs) volume fraction is graded through the thicknesses of face sheets according to a generalized power–law distribution. The material properties of the FG nanocomposite sandwich beam are estimated using the Eshelby–Mori–Tanaka approach based on an equivalent fiber. The equations of motion are derived based on Timoshenko beam theory and employing Hamiltons principle. Generalized differential quadrature technique as an efficient and accurate numerical tool is employed to obtain the natural frequencies of the structure. The verification study represents the accuracy of the solution for free vibration analysis of the nanocomposite sandwich beams resting on elastic foundation. Detailed parametric studies are carried out to investigate the influences of CNTs agglomeration, different profiles of CNT volume fraction such as symmetric, asymmetric, and classic, Winkler foundation modulus, shear elastic foundation modulus, length to span ratio, thicknesses of face sheets, and boundary conditions on the vibrational behavior of the structure. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. Results also represent the fact that utilizing FG nanocomposite sandwich beams in most agglomeration states improves the fundamental frequencies of the structure, but in some cases has a destructive effect on the vibrational characteristics.

Accurate damping analysis of viscoelastic composite beams and plates on suppressive foundation

An accurate study for dynamic behavior of viscoelastic thin laminated composite beams and plates resting on viscoelastic foundations is presented. Boltzmann superposition integral based on the dynamic mechanical analysis results is adapted to accurately predict viscoelastic behavior of polymeric fiber-reinforced composite structures. Also, foundation viscoelasticity is described based on the Kelvin–Voigt model. Integro-differential governing equations of motion are derived based on classical lamination theory via Hamilton principle. Galerkin weighted residual method, iterative QZ algorithm, and Fourier transform are applied to obtain natural frequency, loss factor, and transient response of structures resting on suppressive foundations. Influence of foundation and geometrical parameters and also boundary conditions on the dynamic behavior is put into evidence via a parametric study, and pertinent conclusions are outlined. Due to the absence of similar results in the literature, this paper is likely to fill a gap in the state of the art of this problem.

FREE VIBRATION ANALYSIS AND DESIGN OPTIMIZATION OF SMA/GRAPHITE/EPOXY COMPOSITE SHELLS IN THERMAL ENVI-RONMENTS

COMPOSITE SHELLS, WHICH ARE BEING WIDELY USED IN ENGINEERING APPLICA-TIONS, ARE OFTEN UNDER THERMAL LOADS. THERMAL LOADS USUALLY BRING THER-MAL STRESSES IN THE STRUCTURE WHICH CAN SIGNIFICANTLY AFFECT ITS STATIC AND DYNAMIC BEHAVIOR. ONE OF THE POSSIBLE SOLUTIONS FOR THIS MATTER IS EM-BEDDING SMA WIRES INTO THE STRUCTURE. IN THE PRESENT STUDY, THERMAL BUCKLING AND FREE VIBRATION OF LAMINATED COMPOSITE CYLINDRICAL SHELLS REINFORCED BY SHAPE MEMORY ALLOY (SMA) WIRES ARE ANALYZED. BRINSON MODEL IS IMPLEMENTED TO PREDICT THE THERMO-MECHANICAL BEHAVIOR OF SMA WIRES. THE NATURAL FREQUENCIES AND BUCKLING TEMPERATURES OF THE STRUCTURE ARE OBTAINED BY EMPLOYING GENERALIZED DIFFERENTIAL QUADRA-TURE (GDQ) METHOD. GDQ IS A POWERFUL NUMERICAL APPROACH WHICH CAN SOLVE PARTIAL DIFFERENTIAL EQUATIONS. A COMPARATIVE STUDY IS CARRIED OUT TO SHOW THE ACCURACY AND EFFICIENCY OF THE APPLIED NUMERICAL METHOD FOR BOTH FREE VIBRATION AND BUCKLING ANALYSIS OF COMPOSITE SHELLS IN THERMAL ENVIRONMENT. A PARAMETRIC STUDY IS ALSO PROVIDED TO INDICATE THE EFFECTS OF LIKE SMA VOLUME FRACTION, DEPENDENCY OF MATERIAL PROP-ERTIES ON TEMPERATURE, LAY-UP ORIENTATION, AND PRE-STRAIN OF SMA WIRES ON THE NATURAL FREQUENCY AND BUCKLING OF SHAPE MEMORY ALLOY HYBRID COMPOSITE (SMAHC) CYLINDRICAL SHELLS. RESULTS REPRESENT THE FACT THAT SMAS CAN PLAY A SIGNIFICANT ROLE IN THERMAL VIBRATION OF COMPOSITE SHELLS. THE SECOND GOAL OF PRESENT WORK IS OPTIMIZATION OF SMAHC CY-LINDRICAL SHELLS IN ORDER TO MAXIMIZE THE FUNDAMENTAL FREQUENCY PA-RAMETER AT A CERTAIN TEMPERATURE. TO THIS END, AN EIGHT-LAYER COMPOSITE SHELL WITH FOUR SMA-REINFORCED LAYERS IS CONSIDERED FOR OPTIMIZATION. THE PRIMARY OPTIMIZATION VARIABLES ARE THE VALUES OF SMA ANGLES IN THE FOUR LAYERS. SINCE THE OPTIMIZATION PROCESS IS COMPLICATED AND TIME CONSUMING, GENETIC ALGORITHM (GA) IS PERFORMED TO OBTAIN THE ORIENTA-TIONS OF SMA LAYERS TO MAXIMIZE THE FIRST NATURAL FREQUENCY OF STRUC-TURE. GA IS AN EVOLUTIONARY COMPUTATION METHOD BASED ON DARWINIAN THEORIES THAT SOLVES OPTIMIZATION PROBLEMS WITHOUT USING GRADIENT-BASED INFORMATION ON THE OBJECTIVE FUNCTIONS. THE OPTIMIZATION RESULTS SHOW THAT USING AN OPTIMUM STACKING SEQUENCE FOR SMAHC SHELLS CAN INCREASE THE FUNDAMENTAL FREQUENCY OF THE STRUCTURE BY A CONSIDERABLE AMOUNT.

A robust macroscopic model for normal–shear coupling, asymmetric and anisotropic behaviors of polycrystalline SMAs

The aim of this article is to develop a robust macroscopic bi-axial model to capture self-accommodation, martensitic transformation/orientation/reorientation, normal–shear deformation coupling and asymmetric/anisotropic strain generation in polycrystalline shape memory alloys. By considering the volume fraction of martensite and its preferred direction as scalar and directional internal variables, constitutive relations are derived to describe basic mechanisms of accommodation, transformation and orientation/reorientation of martensite variants. A new definition is introduced for maximum recoverable strain, which allows the model to capture the effects of tension–compression asymmetry and transformation anisotropy. Furthermore, the coupling effects between normal and shear deformation modes are considered by merging inelastic strain components together. By introducing a calibration approach, material and kinetic parameters of the model are recast in terms of common quantities that characterize a uniaxial phase kinetic diagram. The solution algorithm of the model is presented based on an elastic-predictor inelastic-corrector return mapping process. In order to explore and demonstrate capabilities of the proposed model, theoretical predictions are first compared with existing experimental results on uniaxial tension, compression, torsion and combined tension–torsion tests. Afterwards, experimental results of uniaxial tension, compression, pure bending and buckling tests on rods and tubes are replicated by implementing a finite element method along with the Newton–Raphson and Riks techniques to trace non-linear equilibrium path. A good qualitative and quantitative correlation is observed between numerical and experimental results, which verifies the accuracy of the model and the solution procedure.

Passive vibration control of plate structures using shape memory alloy ribbons

Problems associated with the modeling and vibration control of rectangular plates under dynamic loads with integrated polycrystalline NiTi shape memory alloy (SMA) ribbons are developed. In order to simulate the thermo-mechanical behavior of SMA ribbons under dominant axial and transverse shear stresses, a robust macroscopic constitutive model is introduced. The model is able to accurately predict martensite transformation/orientation, shape memory effect, pseudo-elasticity and in particular reorientation of martensite variants and ferro-elasticity features. The structural model is based on the adoption of the first-order shear deformation theory and on the geometrical non-linearity in the von Kármán sense. Towards obtaining the governing equations of motion, the Hamilton principle is used. Finite element and Newmark methods along with an iterative incremental process based on the elastic-predictor inelastic-corrector return mapping algorithm are implemented to solve the non-linear governing equations in spatial and time domains. Numerical simulations highlighting the implications of pre-strain state and temperature of the SMA ribbons, as well as those related to the respective dynamic loads, are presented and discussed in detail. It is found that the modeling of ferro-elasticity in the dynamic analysis of SMA composite structures could lead to significant conclusions concerning the passive vibration control capability of low-temperature SMA ribbons.

SMA bellows as reversible thermal sensors/actuators

In this paper, the feasibility of reversible bellows made of shape memory alloys (SMAs) in sensory and actuated applications to transfer pressure and/or temperature into a linear motion is investigated. An analytical three-dimensional model is developed to simulate key features of SMAs including martensitic transformation, reorientation of martensite variants, the shape memory effect, and pseudo-elasticity. Axisymmetric two-dimensional theory of thermo-inelasticity based on the non-linear Green–Lagrange strain tensor is employed to derive the equilibrium equations. A finite element method along with an iterative incremental elastic-predictor–inelastic-corrector procedure is developed to solve the governing equations with both material and geometrical non-linearities. The feasibility of reversible SMA bellows in transferring pressure and/or temperature into a linear motion is numerically demonstrated. In this respect, the effects of geometric parameters, magnitude of thermo-mechanical loadings and end conditions on the performances of SMA bellows are evaluated and discussed in depth. This study provides pertinent results toward an efficient and reliable design of reversible thermally-driven SMA bellows.