• Steel and Composite Structures
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• v.35 no.5
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• pp.671-685
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• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.4
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• pp.134-139
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• 2008

A spirally arrayed nano-pattern is designed as a model pattern for the next generation optical storage media. The pattern consists off types of embossed rectangular dot, which are 50nm, 100nm, 150nm and 200nm in length and 50nm in width. The height of the dot is designed to be 50nm. The pitch of the spiral track of the pattern is 100nm. A ER(Electron resist) master for this pattern is fabricated by e-beam lithography process. The ER is first spin-coated to be 50nm thick on a Si wafer and then the model pattern is written on the coated ER layer by e-beam. After developing this pattern written wafer in the solution, a ER pattern master is fabricated. The most conventional e-beam machine can write patterns in orthogonal way, so we made our own pattern generator which can write the pattern in circular or spiral way. This program generates the patterns to be compatible with the e-beam machine from Raith(Raith 150). To fabricate 50nm pattern master precisely, a series of experiments were done including the design compensation for the pattern size, optimization of the dose, acceleration voltage, aperture size and developing. Through these experiments, we conclude that the higher accelerating voltages and smaller aperture size are better for mastering the nano pattern which is in order of 50nm. With the optimized e-beam lithography process, a spiral arrayed 50nm pattern master adopting PMMA resist was fabricated to have dimensional accuracy over 95% compared to the designed. Using this pattern master, a metal pattern stamp will be fabricated by Ni electro plating for injection molding of the patterned plastic substrate.

• Smart Structures and Systems
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• v.12 no.5
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1311-1320
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• 2000

In this study, shape memory alloy(SMA) wires and piezoceramic actuators(PZT's) are employed in order to generate higher modes on the beam deformations. Compressive force is generated and applied to the beam by the pre-strained SMA wires attached at both ends of the beam. PZT's apply concentrated moments to several locations on the beam. Combinations of the compressive force and concentrated moments are investigated in order to understand the higher-mode deformation of beams. The first desired mode shape is obtained by controlling the temperature of the SMA wires. The first and third mode shapes are performed experimentally by heating SMA wires up to phase transformation temperature. The adaptive wing is defined as a wing whose shape parameters such as the camber, wing twist and thickness can be varied in order to change the wing shape for various flight conditions. In this research, control of the camber has been studied. The wing model consists of three plates and many ribs. Two of the plates are placed parallel to each other and they are clamped at one edge. Third plate connects the other edges of the parallel plates together. Each rib is made of SMA wire and connected to the parallel plates. It generates concentrated force and applies to the plates in oblique directions. The PZT's are bonded onto the plates and exert concentrated moments upon the plate at several locations. The object of this research is to generate various shape of wing by combining the concentrated forces and moments.

• Computers and Concrete
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• v.34 no.4
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• pp.447-476
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• 2024

The current research proposes an innovative finite element model established within the context of higher-order beam theory to examine the bending and buckling behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams resting on Winkler-Pasternak elastic foundations. This two-node beam element includes four degrees of freedom per node and achieves inter-element continuity with both C¹ and C⁰ continuities for kinematic variables. The isoparametric coordinate system is implemented to generate the elementary stiffness and geometric matrices as a way to enhance the existing model formulation. The weak variational equilibrium equations are derived from the principle of virtual work. The mechanical properties of FG-CNTRC beams are considered to vary gradually and smoothly over the beam thickness. The current investigation highlights the influence of porosity dispersions through the beam cross-section, which is frequently omitted in previous studies. For this reason, this analysis offers an enhanced comprehension of the mechanical behavior of FG-CNTRC beams under various boundary conditions. Through the comparison of the current results with those published previously, the proposed finite element model demonstrates a high rate of efficiency and accuracy. The estimated results not only refine the precision in the mechanical analysis of FG-CNTRC beams but also offer a comprehensive conceptual model for analyzing the performance of porous composite structures. Moreover, the current results are crucial in various sectors that depend on structural integrity in specific environments.

• Steel and Composite Structures
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• v.48 no.4
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• pp.405-417
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• 2023

In order to strengthen the reinforced concrete T-beams having insufficient shear strength, several strengthening techniques are available in the literature. In this study, three different strengthening strategies were numerically studied. First one is affixing steel plates to the beam surfaces. Second one includes tightening external steel bars vertically similar to beam stirrups. The last one is simultaneous application of these two strengthening procedures which is particularly proposed in this work. Available experimental test series in the literature were handled in the study. Finite element (FE) models of reinforced concrete beam specimens having sufficient (Beam-1) and low shear capacity (Beam-2) were created within ABAQUS environment. Strengthened beams with different techniques were also modelled to reflect improved shear capacity. FE simulations made it possible to investigate parameters that were not examined during the previous experimental studies. The results of the analyses were then compared and found consistent with the experimentally obtained data. Experimental and FEM analysis results are in agreement between 1% (closest) and 6%. (maximum). Beam-2 was stregthened with 5 new porposed methods. The rate of increase in shear strength varies between 33% and 64%. It was found that, the strengthening techniques were fairly useful in improving the shear capacity of the considered girder. The model with the proposed strengthening alternative has accomplished a higher load carrying capacity, ductility and stiffness than all of the other models.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• Smart Structures and Systems
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• v.26 no.3
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• pp.391-401
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• 2020

The present article reports the feasibility of the electrical energy generation from ambient low-frequency vibration using a piezoelectric material mounted on a bimorph cantilever beam actuator. A corresponding higher-order analytical model is developed using MATLAB in conjunction with finite element method under low-frequency with both damped and undamped conditions. An alternate model is also developed to check the material and dimensional viability of both piezoelectric materials (mainly focussed to PVDF and PZT) and the base material. Also, Genetic Algorithm is implemented to find the optimum dimensions which can produce the higher values of voltage at low-frequency frequencies (≤ 100 Hz). The delamination constraints are employed to avoid inter-laminar stresses and to increase the fracture toughness. The delamination has been done using a Teflon sheet sandwiched in between base plates and the piezo material is stuck to the base plate using adhesives. The analytical model is tested for both homogenous and isotropic material characteristics of the base material and extended to investigate the effect of the different geometrical parameters (base plate dimensions, piezo layer dimensions and placement, delamination thickness and placement, excitation frequency) on the model responses of the bimorph cantilever beam. It has been observed that when the base material characteristics are homogenous, the efficiency of the model remains higher when compared to the condition when it is of isotropic material. The necessary convergence behaviour of the current numerical model has been established and checked for the accuracy by comparing with available published results. Finally, using the results obtained from the model, a prototype is fabricated for the experimental validation via a suitable circuit considering Glass fibre and Aluminium as the bimorph material.

• Journal of Ocean Engineering and Technology
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• v.35 no.3
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• pp.191-202
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• 2021

Studies on very large offshore structures are increasing owing to the development of deep sea, large-scale energy generation using ocean resources, and so on. The enlargement of offshore structures makes the hydroelastic effect and low natural frequency related responses important. Numerical analyses and model tests for hydroelastic and higher-order springing responses of fixed cylindrical structures are conducted in this study. The panel methods with and without the hydroelastic effect with shell elements, and the Morison analysis method with beam elements are applied. To observe the hydroelastic effect for structural strength, two structures are considered: bottom-fixed cylindrical structures with high and low bending stiffnesses, respectively. The surge motions at the top of the structure and bending stresses on the structure are observed under regular and irregular wave conditions. The regular wave conditions are generated considering the ratios of the cylindrical outer diameter to the wave lengths, and keeping the wave steepness constant. The model tests are performed in the three-dimensional ocean engineering basin in the KRISO (Korea Research Institute of Ships and Ocean Engineering). From the numerical and experimental results, in which the hydroelastic responses are only observed in the case of the structure with a low bending stiffness, it is confirmed that the hydroelastic responses are highly dependent on the structural stiffness. Additionally, the higher-order phenomenon on the specified wave condition is analyzed by observing the higher-order springing responses when the incident wave frequency or its multiples with the high wave height coincides with the natural frequency of the structure.

• Advances in nano research
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• v.16 no.3
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• pp.289-301
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• 2024

In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.