Article
Engineering, Multidisciplinary
Chao Zhou, Dongqi An, Jianyu Zhou, Zixuan Wang, Rui Li
Summary: This paper introduces a novel approach for exploring analytic buckling solutions of non-Levy-type moderately thick rectangular plates, providing a solid foundation for exploring new solutions of similar problems due to its strictness and accuracy.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Engineering, Civil
Yongan Ren, Ruili Huo, Ding Zhou
Summary: This paper investigates the thermo-mechanical buckling behavior of a rectangular plate with temperature-dependent material properties under non-uniform heating. The buckling analysis is performed using the differential quadrature method, including three steps: proposing a 2D non-linear heat transfer equation to obtain the temperature distribution, solving the thermoelastic equilibrium equation to obtain the in-plane stress distribution, and determining the critical load by solving the stability equation. The results are compared with finite element solutions and literature data, showing good agreement. The effects of surrounding temperature fields and in-plane load cases on the thermo-mechanical behavior of the plate are analyzed in detail.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Civil
Xiaolan Xu, Dongdong Wang, Xiwei Li, Songyang Hou, Jianguo Zhang
Summary: A superconvergent isogeometric method has been developed for the buckling analysis of thin beams and plates, optimizing numerical integration rules to improve the accuracy of buckling loads. The method shows higher accuracy and efficiency in computational buckling load analysis.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2021)
Article
Engineering, Mechanical
S. Moradi Haghighi, A. Alibeigloo
Summary: This paper investigates the thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) using the third-order shear deformation theory (TSDT). The CNTs are distributed uniformly or functionally graded along the thickness direction of the plate. The properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations are derived using the Hamilton principle and solved using Fourier series expansion and the differential quadrature method. The study examines the effects of CNT volume fraction, distribution patterns, temperature difference, aspect ratio, and thickness-to-length ratio on the buckling and vibration behavior of the carbon nanotube-reinforced composite plate. The numerical results show that the FG-X pattern of CNT distribution has a significant impact on natural frequency and thermal buckling load.
JOURNAL OF ENGINEERING MECHANICS
(2023)
Article
Mechanics
Mojtaba Derikvand, Fatemeh Farhatnia, Dewey H. Hodges
Summary: The purpose of this study is to investigate the buckling characteristics of a sandwich beam with a porous ceramic core and different layers. The study takes into account shear deformation effects and uses the differential transform method to solve the equilibrium equations. The results show that the critical buckling load is highest for the beam with an asymmetric pattern in the porous ceramic core.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Engineering, Mechanical
Zhaoyang Hu, Xinran Zheng, Dongqi An, Chao Zhou, Yushi Yang, Rui Li
Summary: This paper presents a first attempt to extend an up-to-date symplectic superposition method to linear buckling of side-cracked rectangular thin plates. The problems are introduced into the Hamiltonian system, and a side-cracked plate is then divided into several sub-plates that are analytically solved by the symplectic superposition method. The final analytic solution of a side-cracked plate is obtained by integration of the solutions of the sub-plates, providing a rational approach to exploring more analytic solutions without predetermination of solution forms.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Engineering, Civil
Sijun Xiong, Chao Zhou, Liang Zhao, Xinran Zheng, Yan Zhao, Bo Wang, Rui Li
Summary: This paper presents new analytic thermal buckling solutions for temperature-dependent moderately thick functionally graded rectangular plates with non-Levy-type constraints. The solutions are derived within the symplectic solution framework in the Hamiltonian system, using variable separation and symplectic eigen expansion. The results are validated through benchmark calculations and provide insights into the effects of various geometric parameters on buckling temperatures.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2022)
Article
Mechanics
Majid Afzali, Mojtaba Farrokh, Erasmo Carrera
Summary: This study numerically analyzes the thermal post-buckling response of rectangular functionally graded (FG) plates. An accurate numerical method is used to compute the temperature distribution across the thickness in a thermal environment. Geometrically nonlinear analysis is performed using the Carrera Unified Formulation (CUF) and the finite element method (FEM) based on large displacement assumption. The results show the influence of various parameters on the temperature-deflection path of FG plates and confirm the effectiveness of using CUF for thermal post-buckling analysis.
COMPOSITE STRUCTURES
(2023)
Article
Engineering, Civil
Yu-fang Zheng, Chong-chun Kang, Liang-liang Xu, Chang-ping Chen
Summary: Based on the first-order shear deformation theory and von Karman's nonlinear strain-displacement relationship, a nonlinear dynamic model of rectangular magnetoelectroelastic (MEE) laminated plate is established. Nonlinear motion control equations are derived using Hamilton's principle. By introducing dimensionless parameters, these equations are processed into dimensionless form. The influences of size factors, temperature variation, stacking sequence, and external loads on plate deflection are studied, and the distribution rule of electric and magnetic potential along the plate thickness direction is given for different stacking sequences of the MEE laminated plate.
THIN-WALLED STRUCTURES
(2022)
Article
Engineering, Civil
J. Tenenbaum, M. Eisenberger
Summary: This paper derives analytical solutions for the buckling loads of thin rectangular plates with internal supports and different boundary conditions. The analytical method is based on developing a static solution for the plate. Buckling is defined as the loss of stiffness, where zero force on the plate surface generates infinite displacement. Using this new method, exact buckling loads and modes are obtained for various cases of plates with different boundary conditions and internal supports.
THIN-WALLED STRUCTURES
(2021)
Article
Mechanics
H. Farahmand, P. Yasaie
Summary: This study investigates the buckling analysis of moderately thick porous micro-plate using strain gradient theory and two-variable strain gradient theory. Analytical solutions are obtained, and the effects of thickness, porosity, etc., on the critical buckling load are examined. Increasing thickness shows significant differences between TV-SGT and classical theory results, and porosity has a notable influence on the critical buckling load.
ARCHIVE OF APPLIED MECHANICS
(2021)
Article
Engineering, Aerospace
X. L. Zhang, X. C. Chen, M. Li, Y. H. Li, J. Xu
Summary: This paper investigates the thermal post-buckling behaviors of magneto-electro-elastic laminated beams, modeling the beams using Timoshenko beam theory with von Karman geometric nonlinearity. The study focuses on thermal post-buckling paths, post-buckling vibration characteristics, and magneto-electric potential responses, discussing the effects of lay-up modes, thermal load types, and magneto-electric fields.
AEROSPACE SCIENCE AND TECHNOLOGY
(2021)
Article
Engineering, Civil
He Liu, Hongzhi Zhong
Summary: A weak form quadrature element formulation is proposed for the analysis of elastic buckling in thin plates with side cracks. The problem domain is divided into a square subdomain near the crack tip and quadrilateral subdomains elsewhere. The stress distribution is determined in pre-buckling analysis, and the potential energy is computed using asymptotic displacement expansion and weak form quadrature elements. A generalized eigenvalue problem is solved to find the critical loads and buckling modes, and the formulation is validated with numerical examples.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Aerospace
Zhaoyang Hu, Chao Zhou, Zhuofan Ni, Xinran Zheng, Zixuan Wang, Dian Xu, Bo Wang, Rui Li
Summary: Analytical solutions for elastoplastic buckling of plates are important for benchmark results and fast structural analyses. However, existing solutions are incomplete due to mathematical difficulties and material nonlinearity. This study extends a novel method to obtain new analytical solutions for non-Levy-type rectangular plates and investigates the differences between incremental theory and deformation theory in predicting buckling loads. The findings provide useful guidelines for analyses and designs.
Article
Mechanics
Li-Cai Zhao, Shi-Shuenn Chen, Jiaxing Cheng
Summary: This paper investigates the thermal buckling behavior of damaged rectangular thin plates using the continuum damage mechanics approach. The stability equilibrium equations of damaged rectangular plates under thermal loads are derived based on classical plate theory. Analytical solutions for the temperature variation function and the effects of geometry size on the buckling temperature are obtained using a concrete rectangular plate with damage on four edges simply supported under pressure as an example. The numerical results show that considering material damage in thermal buckling analysis is more in line with engineering practice and improves design requirements of reliability. The correctness of the numerical results is verified through a comparison with the existing results.
ARCHIVE OF APPLIED MECHANICS
(2022)
Article
Mechanics
Chunhua Jin, Xinwei Wang
COMPOSITE STRUCTURES
(2015)
Article
Mathematics, Applied
Chunhua Jin, Xinwei Wang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2015)
Article
Engineering, Mechanical
Xinwei Wang, Yu Wang
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2015)
Article
Mechanics
Xinwei Wang, Yu Wang
COMPOSITE STRUCTURES
(2016)
Article
Engineering, Civil
Xinwei Wang, Yu Wang, Luyao Ge
THIN-WALLED STRUCTURES
(2016)
Article
Engineering, Aerospace
Ansar Mahmood, Xinwei Wang, Chuwei Zhou
AEROSPACE SCIENCE AND TECHNOLOGY
(2013)
Article
Engineering, Multidisciplinary
Xinwei Wang, Yongliang Wang, Zhangxian Yuan
APPLIED MATHEMATICAL MODELLING
(2014)
Article
Mathematics, Applied
Xinwei Wang, Zhe Wu
APPLIED MATHEMATICS AND COMPUTATION
(2013)
Article
Mathematics, Applied
Guohui Duan, Xinwei Wang
APPLIED MATHEMATICS AND COMPUTATION
(2013)
Article
Mathematics, Applied
Xinwei Wang, Guohui Duan
APPLIED MATHEMATICS AND COMPUTATION
(2014)
Article
Mathematics, Applied
Chunhua Jin, Xinwei Wang, Luyao Ge
APPLIED MATHEMATICS LETTERS
(2014)
Article
Mechanics
Yu Wang, Xinwei Wang
COMPOSITE STRUCTURES
(2014)
Article
Engineering, Mechanical
Guohui Duan, Xinwei Wang
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2014)
Article
Engineering, Civil
Guohui Duan, Xinwei Wang, Chunhua Jin
THIN-WALLED STRUCTURES
(2014)
Article
Acoustics
Luyao Ge, Xinwei Wang, Chunhua Jin
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)