Hierarchical one-dimensional finite elements for the thermal stress analysis of three-dimensional functionally graded beams

Pietro, G. De; Hui, Yilong; Giunta, Gaetano; Belouettar, Salim; Carrera, Erasmo; Hu, Heng

doi:10.1016/j.compstruct.2016.06.012

Cited by 20 publications

(7 citation statements)

References 25 publications

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“…Sandwich beams present a complex stress state due to the high difference in stiffness between face-sheets and core. In comparison with previous studies on isotropic, laminated and functionally graded beams by means of the same finite element formulation [40,41], a reduced accuracy of results is observed for sandwich beams, due to the limits of an equivalent single layer approach in modelling such structures. Nevertheless, the presented numerical investigations have demonstrated that the relative errors on the displacements and stresses can be as high as 5% and 7%, respectively, for all the considered load and constraint configurations.…”

Section: Discussionmentioning

confidence: 70%

A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling

Pietro

Giunta

Belouettar

et al. 2017

Jnl of Sandwich Structures & Materials

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A static analysis of three-dimensional sandwich beam structures using one-dimensional modelling approach is presented within this paper. A family of several one-dimensional beam elements is obtained by hierarchically expanding the displacements over the cross-section and letting the expansion order a free parameter. The finite element approximation order over the beam axis is also a formulation free parameter (linear, quadratic and cubic elements are considered). The principle of virtual displacements is used to obtain the problem weak form and derive the beam stiffness matrix and equivalent load vectors in a nuclear, generic form. Displacements and stresses are presented for different load and constraint configurations. Results are validated towards three-dimensional finite element solutions and experimental results. Sandwich beams present a three-dimensional stress state and higher-order models are necessary for an accurate description. Numerical investigations show that fairly good results with reduced computational costs can be obtained by the proposed finite element formulation.

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Section: Discussionmentioning

confidence: 70%

A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling

Pietro

Giunta

Belouettar

et al. 2017

Jnl of Sandwich Structures & Materials

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“…After many experimental studies, it seems that a new theory is needed to analyze such systems. The size-dependent static and vibration behaviors in micro-scales have experimentally been confirmed [ 17 , 18 , 19 , 20 ]. Torsion and tension experiments [ 21 ] and micro-bend test [ 22 ] have been designed to prove the size-dependent behaviors.…”

Section: Introductionmentioning

confidence: 98%

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

et al. 2017

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Micro functionally graded material (FGM) structures are able to have proper functions in vast environments. In this paper, nonlinear governing equations of the size-dependent micro-switch are derived using modified couple stress theory. Effective external forces including fringing field of electrostatic force and Casimir force are considered. Two electrodes cooperate to track the in-plane motions of the micro continuous system by tuning the supply voltages of the electrostatic force. An adaptive projection law is proposed to compensate for the effect of error in the initial estimates of system parameters. To achieve more reliability, a robust active vibration strategy is presented to withstand external disturbances. At any time, just one electrode is operational, and optimization is performed to decrease the controller gains. The highly nonlinear inputs have a singularity in the dynamics of the system, which are known as pull-in instability, so for safety, the controller gains are chosen such that the pull-in voltage is avoided. The dynamic response of the system is simulated using a single mode or multiple modes to validate the effectiveness of the presented vibration control approaches. The effects of error of the initial estimate of system parameters, the effect of impulse and the influences of various volume fractions are studied.

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“…FGMs are often used in structures or applications that commonly operate under extreme temperature and/or environmental conditions, such as spacecrafts, aircrafts, and nuclear reactors [6][7][8]. The main reasons for their use are their outstanding thermo-mechanical properties, corrosion resistance, and high fracture toughness [9].…”

Section: Introductionmentioning

confidence: 99%

Thermal–Structural Linear Static Analysis of Functionally Graded Beams Using Reddy Beam Theory

Murillo

Rivera

Garcia

2023

MCA

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In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in the thickness direction, and the effective material properties are evaluated by means of the rule of mixtures. The volume distribution of the top constituent is modeled using the power law form. A comparison of the present finite element model with the numerical results available in the literature reveals that they are in good agreement. In addition, a routine to study functionally graded plane models in a commercial finite element code is used to verify the performance of the proposed model. In the present work, displacements for different values of the power law exponent and surface temperatures are presented. Furthermore, the normal stress variation along the thickness is shown for several power law exponents of functionally graded beams subjected to thermal and mechanical loads.

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Hierarchical one-dimensional finite elements for the thermal stress analysis of three-dimensional functionally graded beams

Cited by 20 publications

References 25 publications

A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling

A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

Thermal–Structural Linear Static Analysis of Functionally Graded Beams Using Reddy Beam Theory

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