Unsymmetrical large deformation problem of orthotropic plates

2002 ◽  
Vol 23 (9) ◽  
pp. 993-1000 ◽  
Author(s):  
Wang Xin-zhi ◽  
Zhao Yong-gang ◽  
Yeh Kai-yuan ◽  
Huang Da-wen
Keyword(s):  
Large Deformation ◽  
Orthotropic Plates ◽  
Deformation Problem ◽  
Large Deformation Problem

Description of Large Deformation Problem Using Means of Visual Strain

2013 ◽  
Vol 275-277 ◽  
pp. 16-22
Author(s):  
You Liang Xu
Keyword(s):  
Constitutive Equation ◽  
Large Deformation ◽  
Strain Tensor ◽  
Visual Image ◽  
Linear Strain ◽  
Deformation Problem ◽  
Practical Engineering ◽  
Large Deformation Problem ◽  
Strain Tensors ◽  
Linear Strain Tensor

The constitutive equation of large deformation problem is closely related to geometric description. Nowadays, linear strain tensor is no longer unsuitable to describe large deformation. However, the existing non-linear strain tensors have complicated forms as well as no apparent geometric or physical meaning. While, the increment method is used to solve, however, convergence and efficiency are low sometimes. Thus the idea of visual strain tensor is proposed, with distinct meaning and visual image. Beside, it is likely to be used in engineering measurement, and it can be connected with measured constitutive equation directly. Thus this research provides a new idea and method for solving large-deformation problems in practical engineering.

Nonlinear Large Deformation of Graphene Sheets Using a Nonlocal-Based ANCF Method

2019 ◽  
Vol 11 (04) ◽  
pp. 1950037 ◽  
Author(s):  
Qingtao Wang ◽  
Zhen Zhao ◽  
Yang Zhang ◽  
Zhaojun Pang ◽  
Fuzhou Niu
Keyword(s):  
Large Deformation ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Elastic Force ◽  
Graphene Sheets ◽  
Deformation Problem ◽  
Proposed Model ◽  
Large Deformation Problem ◽  
Loading Modes ◽  
Definition Of

A novel nonlinear model of single-layered graphene sheets (SLGSs) subject to large deformation is proposed using the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory. The geometrical definition of SLGSs is described by ANCF thin plate element while the strain energy is expressed by nonlocal theory. Then, the formulation of elastic force and the Jacobian of the elastic force is derived. We verify the proposed model by comparing the results with other published results and conduct corresponding numerical case study to clarify the influence of boundary conditions (BCs), nonlocal parameters, side length and aspect ratio. Large deformation problem of SLGSs with several BCs and different loading modes are simulated to study the mechanical nonlinearity of the SLGSs.

scholarly journals Large Deformation Problem of Bimodular Functionally-Graded Thin Circular Plates Subjected to Transversely Uniformly-Distributed Load: Perturbation Solution without Small-Rotation-Angle Assumption

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2317
Author(s):  
Xue Li ◽  
Xiao-Ting He ◽  
Jie-Chuan Ai ◽  
Jun-Yi Sun
Keyword(s):  
Yield Stress ◽  
Large Deformation ◽  
Rotation Angle ◽  
Functionally Graded ◽  
Governing Equations ◽  
Deformation Problem ◽  
Distributed Load ◽  
Large Deformation Problem ◽  
Small Rotation ◽  
Perturbation Solutions

In this study, the large deformation problem of a functionally-graded thin circular plate subjected to transversely uniformly-distributed load and with different moduli in tension and compression (bimodular property) is theoretically analyzed, in which the small-rotation-angle assumption, commonly used in the classical Föppl–von Kármán equations of large deflection problems, is abandoned. First, based on the mechanical model on the neutral layer, the bimodular functionally-graded property of materials is modeled as two different exponential functions in the tensile and compressive zones. Thus, the governing equations of the large deformation problem are established and improved, in which the equation of equilibrium is derived without the common small-rotation-angle assumption. Taking the central deflection as a perturbation parameter, the perturbation method is used to solve the governing equations, thus the perturbation solutions of deflection and stress are obtained under different boundary constraints and the regression of the solution is satisfied. Results indicate that the perturbation solutions presented in this study have higher computational accuracy in comparison with the existing perturbation solutions with small-rotation-angle assumption. Specially, the computational accuracies of external load and yield stress are improved by 17.22% and 28.79% at most, respectively, by the numerical examples. In addition, the small-rotation-angle assumption has a great influence on the yield stress at the center of the bimodular functionally-graded circular plate.

Modeling of large deformation problem considering spatially variable soils in offshore engineering

2020 ◽  
pp. 1-13
Author(s):  
Jinhui Li ◽  
Wuzhang Luo ◽  
Yinghui Tian ◽  
Yuan Wang ◽  
Mark Jason Cassidy
Keyword(s):  
Large Deformation ◽  
Deformation Problem ◽  
Offshore Engineering ◽  
Large Deformation Problem

Support Size Adjustment Algorithm for Reproducing Kernel Particle Method with Semi-Lagrangian Formulation

2011 ◽  
Vol 368-373 ◽  
pp. 1660-1666
Author(s):  
Han Zhong Luo ◽  
Xue Wen Liu ◽  
Xing Chun Huang
Keyword(s):  
Large Deformation ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Lagrangian Formulation ◽  
Reproducing Kernel Particle Method ◽  
Deformation Problem ◽  
Support Size ◽  
Large Deformation Problem ◽  
Reproducing Kernel Particle ◽  
Size Adjustment

As one of meshfree methods, reproducing kernel particle method (RKPM) is usually associated with semi-Lagrangian formulation for large deformation problem to avoid the failure of one-to-one mapping from current configuration to reference configuration. However, numerical crack may happen for large deformation problem working with semi-Lagrangian formulation, if we keep the support size of reproducing kernel shape function as constant. This paper proposed an algorithm to adjust the support size at every step and some numerical results are presented to demonstrate the improvement by the proposed algorithm. Meanwhile, this algorithm is very easy to implement for coding, which does not add much computational cost.

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