A unified modeling method for dynamic analysis of GPLs-FGP sandwich shallow shell embedded SMA wires with general boundary conditions under hygrothermal loading

2022 ◽  
Vol 250 ◽  
pp. 113439
Author(s):  
Jing Zhao ◽  
Jinzhai Hu ◽  
Tianhao Wang ◽  
Hui Li ◽  
Jialin Guan ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Shallow Shell ◽  
Modeling Method ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Unified Modeling

A Unified Modeling Method for Dynamic Analyses of FGP Annular and Circular Plates with General Boundary Conditions

2021 ◽  
Author(s):  
J. Lu ◽  
X. Hua ◽  
C. Chiu ◽  
X. Zhang ◽  
S. Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Modeling Method ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Circular Plates ◽  
Unified Modeling ◽  
Dynamic Analyses ◽  
Vibration Responses

The porous material is an emerging lightweight material, which is able to reduce structural weight and also keeps the superiority of the structure. Therefore, this work is devoted to the investigation of the functionally graded porous (FGP) annular and circular plates with general boundary conditions. The unified modeling method is proposed by combining the first-order shear deformation theory, the virtual spring technology, the multi-segment partition method, and the semi-analysis Rayleigh–Ritz approach. Afterwards, the convergency and correctness of the proposed method are verified, respectively. The frequency parameters, modal shapes, and forced vibration responses are uniformly calculated based on the proposed method. Finally, the dynamic analyses of the FGP annular and circular plates with different parameters, such as the porosity distribution types, porosity ratios, boundary condition types, geometry parameters, and load types, are conducted in detail. It is found that the reasonable porous design is able to keep the dynamic stability of the structure under different parameter variations.

scholarly journals Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

Dynamic Analysis of T-Shaped Plate with General Boundary Conditions

2013 ◽  
Vol 572 ◽  
pp. 509-512
Author(s):  
Dong Yan Shi ◽  
Qing Shan Wang ◽  
Xian Jie Shi
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Double Fourier Series ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Arbitrary Boundary ◽  
Out Of Plane ◽  
Expansion Coefficients ◽  
Good Agreement

In this investigation, an analytical method is proposed for the dynamic analysis of T-shaped plates with general boundary conditions. Four types of springs are uniformly distributed along each edge, which are used to simulate the transverse shearing forces, bending moments, in-plane longitudinal forces and in-plane shearing forces, respectively. Arbitrary boundary conditions can be readily realized by setting the stiffness of the four types restraining springs. The interactions between the plates have been taken into account at the junction with four types of coupling springs. The in-plane and out-of-plane displacements are invariantly expressed, regardless of boundary conditions, as a new form of double Fourier series with a drastically improved convergence as compared with the traditional Fourier series. The expansion coefficients are considered as the generalized coordinates, and determined using the Rayleigh-Ritz technique. Numerical examples are presented to validate the accuracy and reliability of the proposed method. A good agreement is observed between the current results and FEA results. The present method can be directly extended to more complicated structures with any number of plates.

Dynamic Analysis of Circular Cylindrical Shells With General Boundary Conditions Using Modified Fourier Series Method

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Lu Dai ◽  
Tiejun Yang ◽  
W. L. Li ◽  
Jingtao Du ◽  
Guoyong Jin
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Current Method ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Arbitrary Boundary ◽  
Circular Cylindrical Shells

Dynamic behavior of cylindrical shell structures is an important research topic since they have been extensively used in practical engineering applications. However, the dynamic analysis of circular cylindrical shells with general boundary conditions is rarely studied in the literature probably because of a lack of viable analytical or numerical techniques. In addition, the use of existing solution procedures, which are often only customized for a specific set of different boundary conditions, can easily be inundated by the variety of possible boundary conditions encountered in practice. For instance, even only considering the classical (homogeneous) boundary conditions, one will have a total of 136 different combinations. In this investigation, the flexural and in-plane displacements are generally sought, regardless of boundary conditions, as a simple Fourier series supplemented by several closed-form functions. As a result, a unified analytical method is generally developed for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions including all the classical ones. The Rayleigh-Ritz method is employed to find the displacement solutions. Several examples are given to demonstrate the accuracy and convergence of the current solutions. The modal characteristics and vibration responses of elastically supported shells are discussed for various restraining stiffnesses and configurations. Although the stiffness distributions are here considered to be uniform along the circumferences, the current method can be readily extended to cylindrical shells with nonuniform elastic restraints.

An improved Fourier series solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions

2016 ◽  
Vol 50 (30) ◽  
pp. 4199-4233 ◽  
Author(s):  
Qingshan Wang ◽  
Dongyan Shi ◽  
Qian Liang ◽  
Fazle Ahad
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Vibration Analysis ◽  
Laminated Composite ◽  
Fourier Series Expansion ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Spring Stiffness ◽  
Sector Plate

In this article, the authors presented a unified solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. Regardless of the shapes of the plates and the types of boundary conditions, each displacement and rotation component of the elements is expanded as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the plates. The accuracy, reliability, and versatility of the current solution is fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of free vibration analysis for composite laminated annular sector plate, circular sector plate, annular plate, and circular plate are presented, which may be served as benchmark solution for future computational methods. The effects of the sector angles, layer numbers, and boundary spring stiffness on vibration characteristics of the plates are reported. In addition, the force vibration analysis of the plates is also studied. The influence of the boundary spring stiffness, layer number, orthotropic stiffness ration, and fiber orientation angle on dynamic characteristics of the plates is investigated.

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