scholarly journals Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Peng Liu ◽  
Kun Lin ◽  
Hongjun Liu ◽  
Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Spline Interpolation ◽  
Computational Cost ◽  
Functionally Graded ◽  
Point Method ◽  
Finite Point ◽  
Various Boundary Conditions ◽  
Finite Point Method ◽  
Free Transverse Vibration

A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

scholarly journals A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Tian-Jing Mo ◽  
Jun Huang ◽  
Shuang-Bei Li ◽  
Hai Wu
Keyword(s):  
Thick Plate ◽  
Plate Theory ◽  
Spline Interpolation ◽  
Point Method ◽  
Orthogonal Functions ◽  
Finite Point ◽  
Nonlinear Bending ◽  
Thermal Environments ◽  
Finite Point Method ◽  
Fg Plates

A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

Shape Control of Smart Beams Using PZT and SMA Actuators with the Spline Finite Point Method

2013 ◽  
Vol 444-445 ◽  
pp. 134-140
Author(s):  
Shuang Bei Li ◽  
Lin Jie Jiang ◽  
Chunm Mei Mo ◽  
Rong Qin
Keyword(s):  
Smart Materials ◽  
Shape Control ◽  
Computational Cost ◽  
Smart Structure ◽  
Point Method ◽  
Effective Control ◽  
Finite Point ◽  
Sma Actuators ◽  
Finite Point Method ◽  
Smart Beam

The spline finite point method (SFPM) that is based on the third order shear deformation beam theory (TSDT) is introduced to investigate the shape control of smart beam, which is integrated with PZT and SMA actuators. The governing equations of the smart beam are given by the SFPM and TSDT. The shape control problem is formulated as the problem of minimizing the objective function to study the shape control effects of the smart beam under the different control methods. To demonstrate the less computational cost and higher accuracy of the SFPM, several numerical examples are calculated. The advantages of both smart materials and the effective control of smart structure can be obtained by the hybrid actuators.

Natural Vibration Analysis of Piezoelectric Smart FGM Plate by Spline Finite Point Method

2013 ◽  
Vol 444-445 ◽  
pp. 66-71 ◽  
Author(s):  
Shuang Bei Li ◽  
Jun Huang ◽  
Rong Qin
Keyword(s):  
Electric Field ◽  
Natural Vibration ◽  
Plate Theory ◽  
Computational Cost ◽  
Basic Function ◽  
Point Method ◽  
Parameter Method ◽  
Finite Point ◽  
Finite Point Method ◽  
Piezoelectric Layers

The spline finite point method (SFPM) that is based on the classical laminated plate theory is introduced to investigate the natural vibration of smart FGM plate, which is integrated with piezoelectric layers. The spline basic function that meets different boundary conditions is constructed by the generalized parameter method, and a new dynamic computational scheme for smart FGM plate is established to analysis the natural frequency that considering influence of the axial force, which is generated by the electric field. To demonstrate the less computational cost and higher accuracy of the SFPM, several numerical examples are calculated. The effects of the electric field and the influence of the thickness ratio of piezoelectric layer and substrate on the fundamental frequency are also discussed.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

scholarly journals Real-Time Computer Simulation of Three Dimensional Elastostatics Using the Finite Point Method

2011 ◽  
Vol 110-116 ◽  
pp. 2740-2745
Author(s):  
Kirana Kumara P. ◽  
Ashitava Ghosal
Keyword(s):  
Real Time ◽  
Graphics Processing Unit ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Point Method ◽  
Processing Unit ◽  
Finite Point ◽  
Deformable Solids ◽  
Finite Point Method ◽  
Linear Elastostatics

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

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