• Wind and Structures
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• 제36권2호
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• pp.133-147
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• 2023

The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.

• Steel and Composite Structures
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• 제45권3호
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• pp.349-367
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• 2022

In this research, an approach combining a semi-analytical method and an analytical method is presented to investigate the static and dynamic post-buckling behavior of the sandwich functionally graded (FG) porous cylindrical shells exposed to external pressure. The sandwich cylindrical shell considered is composed of a viscoelastic core and two FG porous (FGP) face layers. The viscoelastic core is made of Kelvin-Voigt-type material. The material properties of the FG porous face layer are considered continuous through each face thickness according to a porosity coefficient and a volume fraction index. Two types of sandwich FG porous viscoelastic cylindrical shells named Type A and Type B are considered in the research. Type A shell has the porosity evenly distributed across the thickness direction, and Type B has the porosity unevenly distributes across the thickness direction. The FG face layers are considered in two cases: outside metal surface, inside ceramic surface (OMS-ICS), and inside metal surface, outside ceramic surface (IMS-OCS). According to Donnell shell theory, von-Karman equation, and Galerkin's method, a discretized nonlinear governing equation is derived for analyzing the behavior of the shells. The explicit expressions for static and dynamic critical buckling loading are thus developed. To study the dynamic buckling of the shells, the governing equation is examined via a numerical approach implementing the fourth-order Runge-Kutta method. With a procedure presented by Budiansky-Roth, the critical load for dynamic post-buckling is obtained. The effects of various parameters, such as material and geometrical parameters, on the post-buckling behaviors are investigated.

• Smart Structures and Systems
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• 제9권6호
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• Steel and Composite Structures
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• 제44권2호
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• 한국전산구조공학회논문집
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• 제15권3호
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• pp.491-499
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• 2002

직교이방성 적층평판해석을 위해 퇴화 쉘요소에 기초를 둔 p-version 유한요소법이 제안되었다. 이 모델의 비선형 정식화과정에서 기하비선형의 경우 von Karman의 대변형-소변형률 가정을 설명하기 위해 Total Lagrangian 방법이 채택되었으며, 재료비선형의 경우 Huber-Mises의 항복기준과 변형률경화 항복함수에 근거를 둔 Prandtl-Reuss 유동법칙이 사용되었다. 재료모델은 이방성을 표현하는 매개변수에 의해 이방겅재료를 고려할 수 있도록 하였다. 적층평판이론으로는 전단변형 효과를 고려할 수 있는 등가단출이론(ESL Theory)에 기초를 두었기 때문에 두 적층간 계면에서의 전단변형률은 연속이라는 조건을 갖게된다 적분형 르장드르 다항식이 형상함수로 사용되었으며 형상함수의 차수는 1차에서 10차까지 변화시킬 수 있다. 또한, Causs-Lobatto 수치적될법을 사용하기 때문에 기존의 가우스 적분점에서 계산되던 응력값은 이 적분법의 적분점이 절점에 위치하므로 절점에서 바로 응력값이 산출되도록 하였다 극한하중 수렴성, 비선형 효과, 소성역의 형상 등의 비교관점을 통해 p-version 유한요소 모델의 적정성을 보이고자 하였다.

• Structural Engineering and Mechanics
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• 제45권5호
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• pp.677-691
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• 2013

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT) or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain-displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton-Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.

• Steel and Composite Structures
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• 제42권6호
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• pp.779-789
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• 2022

This work presents a non-linear cylindrical bending analysis of functionally graded plate reinforced by single-walled carbon nanotubes (SWCNTs) in thermal environment using a simple integral higher-order shear deformation theory (HSDT). This theory does not require shear correction factors and the transverse shear stresses vary parabolically through the thickness. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are considered to be graded in the thickness direction, and are estimated through a micromechanical model. The non-linear strain-displacement relations in the Von Karman sense are used to study the effect of geometric non-linearity and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as benchmarks.