Analysis of cracked shear deformable plates by an effective meshfree plate formulation

Tanaka, Satoyuki; Suzuki, Hirotaka; Sadamoto, Shota; Imachi, Misako; Bui, Tinh Quoc

doi:10.1016/j.engfracmech.2015.06.084

Cited by 91 publications

(21 citation statements)

References 42 publications

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“…The crack length is a and the plate thickness is h. Division of 2728 triangular elements shown in Figure 17 is also employed for this analysis. The normalized SIFs obtained by the present elements for different values of d/b and b/h are presented in Tables 8 and 9, along with reference solutions [68,69]. The numerical methods and plate theories for solving the problem are the same as the above rectangular plate problem involving a center crack.…”

Section: Symmetric Edge Cracks In a Rectangular Platementioning

confidence: 99%

“…The displacement and moment boundary conditions are also illustrated in Figure 17. The numerical results obtained by TrSDTPE, FfSDTPE, and FiSDTPE for different a/h values are reported in Table 7, along with the reference solutions by Tanaka et al [68] and Boduroglu et al [69] based on FSDT for comparison. In Tanaka et al [68], a cracked plate is analyzed by employing the mesh-free reproducing kernel approximation formulated by Mindlin-Reissner plate theory, and the moment intensity factor is evaluated by the J-integral with the aid of nodal integration.…”

Section: Rectangular Plate Involving a Center Crackmentioning

confidence: 99%

“…The numerical results obtained by TrSDTPE, FfSDTPE, and FiSDTPE for different a/h values are reported in Table 7, along with the reference solutions by Tanaka et al [68] and Boduroglu et al [69] based on FSDT for comparison. In Tanaka et al [68], a cracked plate is analyzed by employing the mesh-free reproducing kernel approximation formulated by Mindlin-Reissner plate theory, and the moment intensity factor is evaluated by the J-integral with the aid of nodal integration. In Boduroglu et al [69], the crack problem is solved by the dual boundary element method based on Reissner plate formulation, and the stress resultant intensity factor is calculated by employing the J-integral techniques.…”

Section: Rectangular Plate Involving a Center Crackmentioning

confidence: 99%

See 2 more Smart Citations

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Gou¹,

Cai²,

Zhu³

2018

Applied Sciences

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Featured Application: Due to the mathematical complexity raised by a high continuity requirement, developing simple/efficient standard finite elements with general polynomial approximations applicable for arbitrary HSDTs seems to be a difficult task at the present theoretical level. In this article, a series of High-order Shear Deformation Triangular Plate Elements (HSDTPEs) are developed using polynomial approximation for the analysis of isotropic thick-thin plates, through-thickness functionally graded plates, and cracked plates. The HSDTPEs have the advantage of simplicity in formulation, are free from shear locking, avoid using a shear correction factor and reduced integration, and provide stable solutions for thick and thin plates. The work can be further applied to plates and shells analysis with arbitrary shapes of elements, as well as more general problems related to the shear deformable effect, such as fracture and functionally graded plates. Abstract:The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C 1 continuity in approximation fields in HSDTs brings difficulties for the numerical implementation of the standard finite element method which is similar to that of the classic Kirchhoff-Love plate theory. As a strong complement to HSDTs, in this work, a series of simple High-order Shear Deformation Triangular Plate Elements (HSDTPEs) using incompatible polynomial approximation are developed for the analysis of isotropic thick-thin plates, cracked plates, and through-thickness functionally graded plates. The elements employ incompatible polynomials to define the element approximation functions u/v/w, and a fictitious thin layer to enforce the displacement continuity among the adjacent plate elements. The HSDTPEs are free from shear-locking, avoid the use of a shear correction factor, and provide stable solutions for thick and thin plates. A variety of numerical examples are solved to demonstrate the convergence, accuracy, and robustness of the present HSDTPEs.

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Section: Symmetric Edge Cracks In a Rectangular Platementioning

confidence: 99%

Section: Rectangular Plate Involving a Center Crackmentioning

confidence: 99%

Section: Rectangular Plate Involving a Center Crackmentioning

confidence: 99%

See 1 more Smart Citation

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Gou¹,

Cai²,

Zhu³

2018

Applied Sciences

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“…These methods do not require any discretization of the problem domain, and therefore, the approximate solution of the problem is obtained using a set of scattered nodes. One of the attractions of the meshless methods may be devoted to their flexibility in dealing with discontinuities (such as cracks) [20][21][22][23][24]. The FFEM was firstly developed to calculate the SIFs for cracked domains [25,26].…”

Section: Introductionmentioning

confidence: 99%

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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The existence of crack and notch is a considerable and serious subject in the failure study of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are dominant approaches dealing with fracture mechanics problems. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics, the SIFs may be estimated using the energy release rate, as an indirect approach. This study presents the development of a new semi-analytical method to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature yield diagonal Euler's differential equations. Therefore, when the local coordinate origin is located at the crack tip, the geometry of crack problems is implemented directly without further processing. In order to present crack boundary conditions, a modified form of nodal force function is presented. Validity and accuracy of the proposed method is fully illustrated by four benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature.

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“…Their obtained results were in agreement with those have been obtained from XFEM even were more accurate in some cases. Tanaka et al in 2015 [21] have been developed an effective meshfree formulation for cracked bending plate based on Reissner theory in which the stabilized conforming nodal integration and subdomain conforming integration techniques have been used to integrate the stiffness matrix. For several through the thickness cracked plate problems, the moment stress intensity factors evaluated using the J-integral approach, have been reported and compared to that obtained from the analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

A Cell Centered Finite Volume Formulation for the Calculation of Stress Intensity Factors in Mindlin-Reissner Cracked Plates

Amraei

Fallah

2018

C.E.J

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In fracture analysis, the stress intensity factor (SIF) is an important parameter which is needed for describing the stress state at crack tip. In this paper a finite volume formulation is developed for calculating the stress intensity factor (SIF) in Mindlin-Reissner plates with a through-the-thickness crack (through crack). For approximating the field variables and its derivatives the moving least square (MLS) technique is utilized. The problem domain is discretized into a mesh of elements where each element is considered as a control volume (CV). The center of CVs are considered as computational points where the unknown variables are associated with. The equilibrium equations of each CV are written based on the stress resultant forces acting on the boundaries of CV where the first order shear deformation theory (FSDT) is implemented in the formulation. Some benchmark problems of plate with through cracks are solved by the present method and the obtained results are compared with the results of analytical and XFEM numerical methods in order to demonstrate the accuracy of the present formulation. These comparisons illustrate the accuracy of predictions of the present solution method. Nevertheless, it is found that the formulation is free of shear locking property which greatly facilitates the cracked plates analysis due to its dual capabilities of analyzing both thin and moderately thick cracked plates.

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Analysis of cracked shear deformable plates by an effective meshfree plate formulation

Cited by 91 publications

References 42 publications

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

A Cell Centered Finite Volume Formulation for the Calculation of Stress Intensity Factors in Mindlin-Reissner Cracked Plates

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