A Circumferentially Enhanced Hermite Reproducing Kernel Meshfree Method for Buckling Analysis of Kirchhoff–Love Cylindrical Shells

2015 ◽  
Vol 15 (06) ◽  
pp. 1450090 ◽  
Author(s):  
Dongdong Wang ◽  
Chao Song ◽  
Huikai Peng
Keyword(s):  
Degrees Of Freedom ◽  
Reproducing Kernel ◽  
Virtual Work ◽  
Cylindrical Shells ◽  
Meshfree Method ◽  
Buckling Analysis ◽  
Shape Functions ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Out Of Plane

A circumferentially enhanced Hermite reproducing kernel (HRK) meshfree method is developed for the buckling analysis of Kirchhoff–Love cylindrical shells. In this method, in order to accurately represent the circumferential periodicity of cylindrical shells, the shell mid-surface is first discretized by a set of physical nodes in the two-dimensional parametric space, thereafter another set of dummy nodes are added by a straightforward periodic translation of the physical nodes. Subsequently the meshfree shape functions are constructed using both the physical nodes and the dummy nodes through a periodically linked relationship. The resulting meshfree shape functions exhibit the desired circumferential periodicity. The meshfree shape functions are formulated in the HRK framework which can be degenerated to the standard reproducing kernel (RK) shape functions just by removing the rotational terms. Meanwhile, the cylindrical shell buckling equations are rationally derived from the consistent linearization of the internal virtual work. During the meshfree discretization, the in-plane shell displacements are represented by the conventional RK shape functions, while the out-of-plane shell deflection is approximated by the Hermite meshfree shape functions with both directional and rotational degrees of freedom. The numerical integration of the material as well as the geometric stiffness matrices are carried out by the strain smoothing sub-domain stabilized conforming integration (SSCI) method. Numerical examples show that the proposed approach yields very favorable results for the buckling analysis of cylindrical shells.

scholarly journals An edge-based smoothed finite element for buckling analysis of functionally graded material variable-thickness plates

2021 ◽  
Author(s):  
Tran Trung Thanh ◽  
Tran Van Ke ◽  
Pham Quoc Hoa ◽  
Tran The Van ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Triangular Element ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Graded Material ◽  
Smoothed Finite Element Method ◽  
Edge Based

The paper aims to extend the ES-MITC3 element, which is an integration of the edge-based smoothed finite element method (ES-FEM) with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3 element), for the buckling analysis of the FGM variable-thickness plates subjected to mechanical loads. The proposed ES-MITC3 element is performed to eliminate the shear locking phenomenon and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing the same edge. The numerical results demonstrated that the proposed method is reliable and more accurate than some other published solutions in the literature. The influences of some geometric parameters, material properties on the stability of FGM variable-thickness plates are examined in detail.

An effective meshfree reproducing kernel method for buckling analysis of cylindrical shells with and without cutouts

2017 ◽  
Vol 59 (6) ◽  
pp. 919-932 ◽  
Author(s):  
S. Sadamoto ◽  
M. Ozdemir ◽  
S. Tanaka ◽  
K. Taniguchi ◽  
T. T. Yu ◽  
...  
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Cylindrical Shells ◽  
Buckling Analysis ◽  
Reproducing Kernel Method

scholarly journals Displacement-based multi-modal formulation of Koiter's method applied to cylindrical shells

2021 ◽  
Author(s):  
Saullo G. P. Castro ◽  
Eelco Jansen
Keyword(s):  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Imperfection Sensitivity ◽  
Data Set ◽  
Collaborative Software ◽  
Close Relationship ◽  
Out Of Plane ◽  
Post Buckling ◽  
Displacement Based

The multi-modal formulation of Koiter's asymptotic method provides a systematic and efficient procedure to evaluate the initial post-buckling behaviour and to assess the nonlinear behavior of structures. This manuscript presents a displacement-based multi-modal formulation of Koiter's method for cylindrical shells, which are structures known for their high imperfection sensitivity and for having clustered bifurcation modes that highly interact. A third-order interpolation is used for the in-plane and out-of-plane displacements by means of the Bogner-Fox-Schmit-Castro (BFSC) element, with 4 nodes and 10 degrees-of-freedom per node, aiming at an accurate representation of the second-order fields required in the initial post-buckling analysis. The single-curvature of the shell is considered in the finite element kinematics and the study includes nonlinear kinematics from Von Kármán and Sanders. The mesh is obtained by closing the circumferentially oriented coordinate at the position where the mesh completes one revolution about the shell perimeter. The proposed formulation and implementation is verified in detail by comparing results for composite shells against established literature for multi-mode asymptotic expansions. A fast convergence of the proposed formulation is observed for linear buckling, pre-buckling state and the initial post-buckling coefficients. The developed formulation enables a close relationship between formulae and the implemented code, and is implemented using state-of-the-art collaborative software. The authors made the implemented routines in a publicly available data set with the aim to popularize Koiter's method.

Hermite Reproducing Kernel Meshfree Thermal Buckling Analysis of Euler-Bernoulli Beams with Elastic Foundation

2014 ◽  
Vol 574 ◽  
pp. 85-88
Author(s):  
Chao Song ◽  
Ming Sun ◽  
Bo Ya Dong
Keyword(s):  
Elastic Foundation ◽  
Reproducing Kernel ◽  
Meshfree Method ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Bernoulli Beam ◽  
Meshfree Approximation ◽  
The Stability ◽  
Solution Accuracy ◽  
Euler Bernoulli Beam

The Hermite reproducing kernel meshfree method is employed for the stability analysis of Euler-Bernoulli beams with particular reference to the thermal buckling problem. This meshfree approximation employs both the nodal deflectional and rotational variables to construct the deflectional approximant according to the reproducing kernel conditions. In this paper, we apply this HRK meshfree method to the thermal buckling analysis of Euler-Bernoulli beam on elastic foundation. By comparison to the Gauss Integration method, HRK meshfree method shows much better solution accuracy.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

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