scholarly journals Peridynamic Formulation for Higher-Order Plate Theory

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mixed Boundary ◽  
Lagrange Equation ◽  
Mixed Boundary Conditions ◽  
Higher Order ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Simply Supported ◽  
Peridynamic Model

AbstractIn this study, a new peridynamic model is presented for higher-order plate theory. The formulation is derived by using Euler-Lagrange equation and Taylor’s expansion. The formulation is verified by considering two benchmark problems including simply supported and clamped plates subjected to transverse loading. Moreover, mixed (simply supported-clamped) boundary conditions are also considered to investigate the capability of the current formulation for mixed boundary conditions. Peridynamic results are compared with finite element analysis results and a very good agreement was obtained between the two approaches.

scholarly journals Peridynamic modelling of higher order functionally graded plates

2021 ◽  
pp. 108128652110046
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Higher Order ◽  
Functionally Graded ◽  
Benchmark Problems ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Peridynamic Model

With the development of advanced manufacturing technologies, the importance of functionally graded materials is growing as they are advantageous over widely used traditional composites. In this paper, we present a novel peridynamic model for higher order functional graded plates for various thicknesses. Moreover, the formulation eliminates the usage of shear correction factors. Euler–Lagrange equations and Taylor’s expansion are utilised to derive the governing equations. The capability of the developed peridynamic model is demonstrated by considering several benchmark problems. In these benchmark cases simply supported, clamped and mixed boundary conditions are also tested. The peridynamic results are also verified by their finite element analysis counterparts. According to the comparison, peridynamic and finite element analysis results agree very well with each other.

Implicit Boundary Approach for Reissner-Mindlin Plates

2013 ◽  
Author(s):  
Hailong Chen ◽  
Ashok V. Kumar
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Weak Form ◽  
Mindlin Plate ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Boundary Method ◽  
Solid Models ◽  
Plate Elements ◽  
Background Mesh

Implicit boundary method enables the use of background mesh to perform finite element analysis while using solid models to represent the geometry. This approach has been used in the past to model 2D and 3D structures. Thin plate or shell-like structures are more challenging to model. In this paper, the implicit boundary method is shown to be effective for plate elements modeled using Reissner-Mindlin plate theory. This plate element uses a mixed formulation and discrete collocation of shear stress field to avoid shear locking. The trial and test functions are constructed by utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. The incompatibility of discrete collocation with implicit boundary approach is overcome by using irreducible weak form for computing the stiffness associated with essential boundary conditions. A family of Reissner-Mindlin plate elements is presented and evaluated in this paper using several benchmark problems to test their validity and robustness.

scholarly journals A state-based peridynamic formulation for functionally graded Kirchhoff plates

2020 ◽  
pp. 108128652096338
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Material Properties ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Benchmark Problems ◽  
Transverse Loading ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Kirchhoff Plates ◽  
Peridynamic Model

Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and Taylor’s expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young’s modulus is assumed to be varied linearly through the thickness direction and Poisson’s ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.

A higher-order shell model applied to shells with mixed boundary conditions

2010 ◽  
Vol 225 (2) ◽  
pp. 292-303 ◽  
Author(s):  
M Yaghoubshahi ◽  
E Asadi ◽  
S J Fariborz
Keyword(s):  
Boundary Conditions ◽  
Virtual Work ◽  
Mixed Boundary ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Mixed Boundary Conditions ◽  
Higher Order ◽  
Finite Element Software ◽  
Cylindrical Panels ◽  
Generalized Differential

By means of the principle of virtual work, the governing equations together with the required boundary conditions of a higher-order shear deformation theory are formulated for the analysis of laminated shells under static loads. A system of 31 first-order partial differential equations is performed for the determination of stress resultants and displacement components. These equations are then solved numerically, utilizing the generalized differential quadrature method for two isotropic cylindrical panels with equal arc length but different radii having S2-type simply supported boundary conditions. The results matched those of other theories. Another analysis is carried out for composite cylindrical panels with two lamination schemes, five different mixed boundary conditions, and two length-to-thickness ratios. The results are compared against solutions obtained from ANSYS finite-element software.

A Set of Orthogonal Plate Functions for Flexural Vibration of Regular Polygonal Plates

1991 ◽  
Vol 113 (2) ◽  
pp. 182-186 ◽  
Author(s):  
K. M. Liew ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Mixed Boundary ◽  
Flexural Vibration ◽  
Mixed Boundary Conditions ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simply Supported ◽  
Free Boundary Conditions

A computationally efficient and very accurate numerical method is proposed for vibration analysis of regular polygonal plates with any combinations of clamped, simply-supported and free boundary conditions. The method involves the use of two-dimensional orthogonal polynomials generated by the Gram-Schmidt recurrence procedure. For the cases of simply supported and fully clamped hexagonal and octagonal plates, the results obtained agreed very well with those existing in the literature. The frequencies and mode shapes for several hexagonal and octagonal plates subjected to mixed boundary conditions are also presented.

Shear Buckling of Rectangular Plates with Mixed Boundary Conditions

1963 ◽  
Vol 14 (4) ◽  
pp. 349-356 ◽  
Author(s):  
I. T. Cook ◽  
K. C. Rockey
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Shear Buckling

SummaryThe paper presents a solution for the buckling under shear of a rectangular plate which is clamped along one edge and simply-supported along the other edges. The authors have also re-examined the case of one pair of opposite edges clamped and the other pair simply-supported.

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