Analysis of cracked plate using higher-order shear deformation theory: Asymptotic crack-tip fields and XIGA implementation

Singh, S.K.; Singh, I.V.; Mishra, B.K.; Bhardwaj, Gagandeep

doi:10.1016/j.cma.2018.03.009

Cited by 43 publications

(9 citation statements)

References 73 publications

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“…Although FSDT has been proved to be sufficiently effective and accurate [52], it requires a shear correction factor which is difficult to determine [50]. Various higher order shear deformation theories (HSDTs) have been developed to overcome this difficulty [50,53]. Compared to the solution within the framework of FSDT, the accuracy of the analysis using HSDTs has been slightly improved [50], but the equations of motion in HSDTs are more complicated than those in FSDT [50].…”

Section: Introductionmentioning

confidence: 99%

Fundamental Frequencies of Elliptical Plates using Static Deflections

Altekin¹

2022

Teknik Dergi

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Fundamental frequencies of solid and annular elliptical plates were approximated using the static deflections by means of finite element method (FEM) without computing the eigenvalues. The problem was formulated within the framework of the first order shear deformation theory (FSDT). The effects of (i) the inner and outer boundary conditions, (ii) the size of the perforation, (iii) the aspect ratio, and (iv) the thickness of the plate on the performance of the method were examined via a large variety of numerical simulations. Convergence study was performed through h-refinement. Accuracy of the results was validated through comparison studies. The results reveal that the application of the Morley's formula which does not require eigenvalue analysis approximates the fundamental frequency with finer mesh compared to the eigenvalue analysis. The method can be considered as a practical technique to approximate the fundamental frequency. However, the boundary conditions have dominant role on the accuracy of the solution particularly when the plate is perforated.

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Section: Introductionmentioning

confidence: 99%

Fundamental Frequencies of Elliptical Plates using Static Deflections

Altekin¹

2022

Teknik Dergi

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“…On the basis of the classical plate theory (CPT), these studies have used analytical methods [24,25], the integral equation approach [26,27], the Ritz method [28][29][30][31], the generalized differential quadrature method [32,33], Galerkin's method [34], the mesh-free approach [35], and the FEM [36,37] to investigate the aforementioned vibrations. Based on the first-order shear deformation plate theory (FSDT), studies have developed various approaches, such as the Ritz method [38,39], mesh-free method [40], FEM [41,42], and extended FEM (XFEM) [43,44], while Singh et al [45] used an extended isogeometric approach based on a higher-order shear deformation plate theory.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

Huang

Lee

et al. 2021

Materials

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In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

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“…The XIGA possesses some desirable features besides those in the XFEM, for example, arbitrarily complex structure can be exactly represented, the higher-order continuity of shape functions can be easily obtained, and the traditional mesh generation process is avoided. Due to such excellent characteristics, the XIGA has been applied to solve various discontinuities [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Fang¹,

Yu²,

Yang³

2021

Computer Modeling in Engineering &Amp; Sciences

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Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis (XIGA) method based on locally refined non-uniforms rational B-splines (LR NURBS). In the XIGA, the LR NURBS, which have a simple local refinement algorithm and good description ability for complex geometries, are employed to represent the geometry and discretize the field variables; and some special enrichment functions are introduced into the approximation of temperature field, thus the computational mesh is independent of the material interfaces, which are described with the level set method. Similar to the approximation of temperature field, a temperature gradient recovery technique for heterogeneous media is proposed, and based on the Zienkiewicz-Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions. The convergence and performance properties of the developed method are verified by using three numerical examples. The numerical results show that (1) The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement; (2) The convergence rate of the high-order basis functions is faster than that of the low-order basis functions; and (3) The existing inclusions change the local distributions of the temperature, and the extreme values of the temperature gradients take place around the inclusion interfaces.

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Analysis of cracked plate using higher-order shear deformation theory: Asymptotic crack-tip fields and XIGA implementation

Cited by 43 publications

References 73 publications

Fundamental Frequencies of Elliptical Plates using Static Deflections

Fundamental Frequencies of Elliptical Plates using Static Deflections

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

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