Post buckling analysis of smart laminated doubly curved shells

The variation-difference method is a convenient numerical method for shells of complex forms. It is enough when only cinematic boundary conditions are satisfied because the method is based on the principle of Lagrange. Another advantage of the variation-difference method is the better opportunity to create computer programs based on it. For shell analysis in orthogonal coordinate system as well as for shell analysis in principal curvatures the system of equations describing stress-strain state can be simplified. In this paper the difference between analysis in orthogonal coordinate system and analysis in principal curvatures of the surface is considered. The main distinction of the analysis of shells in orthogonal curvilinear coordinate system is the necessity of determination of components which include curvature of torsion of coordinate lines. The addition of these components in the equations of the theory of shells for the coordinate system in principal curvatures gives possibility to analyze shells in common orthogonal coordinate system. In this article shell analysis in orthogonal coordinate system is applied to shells based on normal cyclic surfaces.

The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Karman’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

Compared with 8-node and 4-node isoparametric element, the 9-node isoparametric element is more flexible and higher rate of convergence. Based on state-space techniques, the 9-node isoparametric element of piezothermoelastic material under orthogonal curvilinear coordinate system is established. Finally, the example shows the practicability and accuracy of the 9-node isoparametric element of piezothermoelastic material under orthogonal curvilinear coordinate system.

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

On the nonlinear-flexural response of piezoelectrically driven microcantilever sensors

This paper focus on the treating the multi freedom constraints in geometrically nonlinear buckling and post buckling analysis of truss structure using finite element method. The solution of geometrically nonlinear buckling problem of truss structure having multi freedom constraints is required to incorporate the boundary constraints to the nonlinear master stiffness equation. This work proposes approach to impose the multi freedom constraints and construct stiffness equation for solving the nonlinear buckling problems of truss structures using Penalty function method. The nonlinear balanced equations for buckling analysis of truss structures are developed by minimization of the augmented potential energy function of system by incorporating the multi freedom constraints and changing the constrained problem to the non-constrained problem using Penalty objective function. Using the arc length method, this research proposes the incremental-iterative algorithm for solving the nonlinear balanced equations. Based on proposed algorithm, the calculation program for determining equilibrium paths is written. The numerical test results show the efficiency of proposed method in analysing buckling and post buckling behaviour of truss structures.

In this paper, static bending analysis of functionally graded plates with piezoelectric layers has been carried out considering geometrical nonlinearity in different sets of mechanical and electrical loadings. Only the geometrical nonlinearity has been taken into account. The governing equations are obtained using potential energy and Hamilton’s principle. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect by using higher order elements. The present finite element used displacement and electric potential as nodal degrees of freedom. Results are presented for two constituent FGM plate under different mechanical boundary conditions. Numerical results for FGM plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response of the plate are also studied.

Smart actuators, made of smart materials, are becoming more attractive in many applications because smart materials are not subjected to wear and does not require lubrication during services. Piezoelectric materials are a group of the many attractive smart materials that are being investigated for many applications today. Piezoelectric materials show fast responses, high efficiency/accuracy and operate on a large bandwidth. Composite materials are of interest because of their design flexibility and because they are lighter than other materials commonly used in aircraft and other applications. For the research reported here, a piezoelectric material was embedded in a composite material to form a piezoelectric composite actuator. This research was conducted to expand our knowledge of piezoelectric composite material actuators, and originated from the need to control air flow separation over an airfoil. There is a need to build a profound knowledge about such actuators before they can be implemented in an airfoil, and to understand which parameters influence the behaviour of piezoelectric composite material actuators under static and dynamic operating conditions. The actuators were manufactured and tested under static and dynamic conditions and the experimental results were compared to the finite element models. The models were incorporated with piezoelectric material properties that were determined experimentally. The results showed that a piezoelectric material’s response to an input stimulant, e.g. electric voltage and frequency, influences the actuator’s behaviour.

The present work deals with the static and vibration behaviour of Smart Functionally Graded (SFG) beams, combined with the piezoelectric material. In this work, the efficiency of Lead Zirconate Titanate (PZT-4) piezoelectric material, attached with the functionally graded (FG) beams, is investigated. Finite element model is made for the FG beam, combined with the piezoelectric material, considering the first order theory (FSDT). The material properties of the FG beam is graded along the direction of its thickness, following the power law distribution method. Simulation model is made employing finite element software (ANSYS) for the functionally graded beams. Different boundary conditions, as well as power law indexes are taken for analysis. The effects of gradation of material properties on static and dynamic behaviour of smart functionally graded beam are studied. The efforts are also made to examine the performance of piezoelectric patches, towards the control of deflections and vibrations.

The handling and control of towed cable and body systems onboard surface ships and submarines presents a significant technical challenge to design engineers in the defense and ocean industries. The current approaches rely heavily on the empirical methods and the time-consuming and costly prototype testing. Computer simulation provides a cost effective way to reduce the high risks associated with the towed cable/body system. However, the current dynamic analysis of towed cables is mostly done by the finite difference (FD) method in stead of the finite element (FE) method that is widely used in almost all engineering fields. This paper presents an alternative FE method to simulate the dynamics of towed cable and body system, in which the large rigid body motion is coupled with small elastic deformation. The newly derived FE method is formulated in terms of element nodal positions, which is different from the existing FE methods that use displacements. The alternative FE method solves for the cable position directly in order to eliminate accumulated numerical errors arising from existing FE methods that solve for displacements first in order to obtain the cable position over very long period of time. The alternative FE formulation is implemented and applied to real applications to demonstrate its robustness by comparing simulation results with the experimental and sea trial data.

The paper considers the regularity problem on three-dimensional incompressible Navier-Stokes equations in general orthogonal curvilinear coordinate systems. We establish one regularity criteria of the weak solutions involving only in a vorticity component ω 3 and one a priori estimate on the solution that H 3 u 3 L ∞ 0 , T ; L p ℝ 3 is bounded for 1 ≤ p ≤ ∞ to three-dimensional incompressible Navier-Stokes equations in orthogonal curvilinear coordinate systems. These extent greatly the corresponding results on axisymmetric cylindrical flow.

In Part I, an analytical examination of electromagnetic boundary conditions at the interface between two different media is presented in an orthogonal curvilinear coordinate system which conforms locally and instantaneously to the interface. Subsequently, an original natural coordinate system is introduced to resolve the uncertainty in the choice of an orthogonal curvilinear coordinate system. This natural coordinate system is also appeared to reduce the number of the nonvanishing discontinuity relations, and to determine local and instantaneous natural aspects of the e.m. boundary conditions problem.

The problem of forced vibration of a hinged beam with piezoelectric layers is solved. Issues of mechanical and electric excitation of vibration and the possibility of damping mechanically induced vibration by applying a voltage to the electrodes of the piezolayers are studied. The effect of the physically nonlinear behavior of the passive layers on the response of the sensor layer and entire structure and the effect of geometric nonlinearity on the behavior of the structure and sensor layer are analyzed. The interaction of physical and geometrical nonlinearities for transient and stationary processes is studied

Tensor analysis and an orthogonal curvilinear coordinate system have been used to derive a complete set of equations for piezo-magneto-elastic analysis of a functionally graded (FG) thick shell of revolution with variable thickness and curvature. The mentioned structure can be subjected to mechanical, electrical and magnetic fields. It was assumed that all material properties (mechanical, electrical and magnetic properties) change functionally throughout the three axis of employed coordinate system. Kinetic and potential energies of the system have been evaluated in order to constitute the functional of the system. Final partial differential equations of the system can be derived by using minimization of the energy functional with respect to five employed functions of the system. For validation, the obtained differential equations have been reduced to two previously studied problems i.e. functionally graded piezoelectric materials and functionally graded piezomagnetic cylinders. Furthermore, numerical results are evaluated for a case study.