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        Differential cubature method for buckling analysis of arbitrary quadrilateral thick plates

        Wu, Lanhe,Feng, Wenjie Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.16 No.3

        In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

      • SCIESCOPUS

        An analytical solution for static analysis of a simply supported moderately thick sandwich piezoelectric plate

        Wu, Lanhe,Jiang, Zhiqing,Feng, Wenjie Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.5

        This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

      • KCI등재
      • SCIESCOPUS

        Thermal vibration analysis of thick laminated plates by the moving least squares differential quadrature method

        Wu, Lanhe Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.22 No.3

        The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

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      • KCI등재

        Computational estimation of the earthquake response for fibre reinforced concrete rectangular columns

        Chanjuan Liu,Xinling Wu,Karzan Wakil,Kittisak Jermsittiparsert,Lanh Si Ho,Hisham Alabduljabbar,Abdulaziz Alaskar,Fahed Alrshoudi,Rayed Alyousef,Abdeliazim Mustafa Mohamed 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.34 No.5

        Due to the impressive flexural performance, enhanced compressive strength and more constrained crack propagation, Fibre-reinforced concrete (FRC) have been widely employed in the construction application. Majority of experimental studies have focused on the seismic behavior of FRC columns. Based on the valid experimental data obtained from the previous studies, the current study has evaluated the seismic response and compressive strength of FRC rectangular columns while following hybrid metaheuristic techniques. Due to the non-linearity of seismic data, Adaptive neuro-fuzzy inference system (ANFIS) has been incorporated with metaheuristic algorithms. 317 different datasets from FRC column tests has been applied as one database in order to determine the most influential factor on the ultimate strengths of FRC rectangular columns subjected to the simulated seismic loading. ANFIS has been used with the incorporation of Particle Swarm Optimization (PSO) and Genetic algorithm (GA). For the analysis of the attained results, Extreme learning machine (ELM) as an authentic prediction method has been concurrently used. The variable selection procedure is to choose the most dominant parameters affecting the ultimate strengths of FRC rectangular columns subjected to simulated seismic loading. Accordingly, the results have shown that ANFIS-PSO has successfully predicted the seismic lateral load with R2 = 0.857 and 0.902 for the test and train phase, respectively, nominated as the lateral load prediction estimator. On the other hand, in case of compressive strength prediction, ELM is to predict the compressive strength with R2 = 0.657 and 0.862 for test and train phase, respectively. The results have shown that the seismic lateral force trend is more predictable than the compressive strength of FRC rectangular columns, in which the best results belong to the lateral force prediction. Compressive strength prediction has illustrated a significant deviation above 40 Mpa which could be related to the considerable non-linearity and possible empirical shortcomings. Finally, employing ANFIS-GA and ANFIS-PSO techniques to evaluate the seismic response of FRC are a promising reliable approach to be replaced for high cost and time-consuming experimental tests.

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