Optimal Control of Random Vibration in Shell Structures With Embedded Piezoelectric Components

2005 ◽  
Author(s):  
Cho W. S. To ◽  
Tao Chen
Keyword(s):  
Finite Element ◽  
Random Vibration ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Shell Structures ◽  
Engineering System ◽  
Hybrid Strain ◽  
Strain Formulation ◽  
Shell Panel ◽  
Shell Finite Element

The state covariance assignment (SCA) method of Skelton and associates is applied in the present investigation to the optimal random vibration control of large scale complicated shell structures with embedded piezoelectric components. It provides a direct approach for achieving performance goals stated in terms of the root-mean-square (RMS) values which are common in many engineering system designs. The large scale shell structures embedded with piezoelectric components of complicated geometrical configurations are approximated by the hybrid strain or mixed formulation based lower order triangular shell finite element developed in the present investigation. This shell finite element has three nodes every one of which has seven degrees of freedom (dof). The latter include three translational dof, three rotational dof, and one electric potential dof. The element is a better alternative to those based on the displacement formulation and that hinged on the truly hybrid strain formulation. Representative results applying the SCA method for a shell panel embedded with piezoelectric components are included to demonstrate its simplicity of use and efficiency of implementing the proposed approach.

Transient Response Analysis of Geometrically Nonlinear Laminated Composite Shell Structures

1996 ◽  
Author(s):  
Cho W. S. To ◽  
Bin Wang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Composite Shell ◽  
Laminated Composite ◽  
Shell Structures ◽  
Response Analysis ◽  
Hybrid Strain ◽  
Drilling Degree Of Freedom ◽  
Shell Finite Element ◽  
Shear Deformable

Abstract The investigation reported in this paper is concerned with the prediction of geometrically large nonlinear responses of laminated composite shell structures under transient excitations by employing the hybrid strain based flat triangular laminated composite shell finite element presented here. Large deformation of finite strain and finite rotation are considered. The finite element has eighteen degrees-of-freedom which encompass the important drilling degree-of-freedom at every node. It is hinged on the first order shear deformable lamination theory. Various laminated composite shell structures have been studied and for brevity only two are presented here. It is concluded that the element proposed is very accurate and efficient. Shear locking has not appeared in the results obtained thus far. There is no zero energy mode detected in the problems studied. For nonlinear dynamic response computations, the full structural system has to be considered if accurate results are required.

Large Geometrically Nonlinear Responses of Discretized Plate Structures Under Nonstationary Random Excitations

1999 ◽  
Author(s):  
C. W. S. To ◽  
M. L. Liu
Keyword(s):  
Finite Element ◽  
Difference Method ◽  
Large Scale ◽  
Hybrid Strain ◽  
Central Difference ◽  
Nonstationary Random Process ◽  
Highly Nonlinear ◽  
Strain Formulation ◽  
Central Difference Method ◽  
Element Matrix

Abstract In the investigation reported here novel techniques for the computation of highly nonlinear response statistics, such as mean square and covariance of generalized displacements of large scale discretized plate and shell structures have been developed. The techniques combine the versatile finite element method and the stochastic central difference method as well as derivatives of the latter such that complex aerospace and naval structures under intensive transient disturbances represented as nonstationary random processes can be considered. The flat triangular plate finite element is of the Mindlin type and is based on the hybrid strain formulation. The updated Lagrangiah hybrid strain based formulation is capable of dealing with deformations of finite rotations and finite strains. Explicit expressions for the consistent element mass and stiff matrices were previously obtained, and therefore no numerical matrix inversion and integration is necessary in the element matrix derivation. Several additional features are novel. First, the so-called averaged deterministic central difference scheme is employed in the co-ordinate updating process for large deformations. Second, application of the time co-ordinate transformation in conjunction with the stochastic central difference method enables one to deal with highly stiff discretized structures. Third, application of the adaptive time schemes makes it convenient to solve a wide variety of highly nonlinear systems. Finally, the recursive nature of the stochastic central difference method makes it possible to deal with a wide class of nonstationary random process.

Nonstationary Random Response of Laminated Composite Structures by a Hybrid Strain-Based Laminated Flat Triangular Shell Finite Element

1995 ◽  
Author(s):  
C. W. S. To ◽  
B. Wang
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Composite Shell ◽  
Laminated Composite ◽  
Random Excitation ◽  
Cylindrical Panel ◽  
Shell Structures ◽  
Hybrid Strain ◽  
Automobile Engineering ◽  
Shell Finite Element

Abstract The prediction and analysis of response of laminated composite shell structures under nonstationary random excitation is of considerable interest to design engineers in aerospace and automobile engineering fields. However, it seems that there is no known comprehensive published work on such an analysis that employs the versatile finite element method. Thus, the main focus of the investigation reported in this paper is the application of the hybrid strain-based laminated composite flat triangular shell finite element, that has been developed by the authors, for the analysis of laminated composite shell structures under a relatively wide class of nonstationary random excitations. Representative results of a simply-supported laminated composite cylindrical panel subjected to a point nonstationary random excitation are included.

Large Nonlinear Responses of Spatially Nonhomogeneous Stochastic Shell Structures Under Nonstationary Random Excitations

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Random Disturbance ◽  
Hybrid Strain ◽  
Central Difference ◽  
Spherical Cap ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Novel Approach ◽  
Random Disturbances

A novel approach for determining large nonlinear responses of spatially homogeneous and nonhomogeneous stochastic shell structures under intensive transient excitations is presented. The intensive transient excitations are modeled as combinations of deterministic and nonstationary random excitations. The emphases are on (i) spatially nonhomogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, (iii) intensive deterministic and nonstationary random disturbances, and (iv) the large responses of a specific spherical cap under intensive apex nonstationary random disturbance. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The novel approach consists of the stochastic central difference method, time coordinate transformation, and modified adaptive time schemes. Computed results of a temporally and spatially stochastic shell structure are presented. Computationally, the procedure is very efficient compared with those entirely or partially based on the Monte Carlo simulation, and it is free from the limitations associated with those employing the perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method. The computed results obtained and those presented demonstrate that the approach is simple and easy to apply.

Some new results and current challenges in the finite element analysis of shells

Acta Numerica ◽  
2001 ◽  
Vol 10 ◽  
pp. 215-250 ◽  
Author(s):  
Dominique Chapelle
Keyword(s):  
Finite Element ◽  
Shell Theory ◽  
Shell Structures ◽  
Engineering Practice ◽  
Element Analysis ◽  
Shell Elements ◽  
Shell Models ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Mathematical Analyses

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

Response of Submerged Structures by the Finite Element-Cum-Boundary Element Method

2001 ◽  
Author(s):  
C. W. S. To ◽  
M. A. O’Grady
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Problem Size ◽  
Hybrid Strain ◽  
Fluid Structure ◽  
Structure Interaction ◽  
High Convergence Rate ◽  
Shell Finite Element

Abstract A double asymptotic approximation based finite element-cum-boundary element approach for fluid-structure interaction problems is being proposed. In particular a staggered solution scheme has been applied to the analysis of various coupled fluid-structure systems. A stabilization scheme by reformulation, proposed by DeRuntz et al. was employed to circumvent the instability problem. In addition, the singularity in the excitation term was eliminated through a variable transformation as suggested by Everstine. Another feature of the present work is its incorporation of the hybrid strain based lower order triangular shell finite element developed by To and Liu. The eigenvalue solution exhibits high convergence rate for the particular shell finite element employed. The responses calculated exhibit the effectiveness of the proposed approach with application of the aforementioned shell finite element in dealing with three dimensional fluid-structure interaction problems. The reduction in problem size that this approach affords allows these complex interaction problems to be dealt with in a desktop engineering workstation environment, as opposed to the mainframe and supercomputer arenas where they have been implemented in the past.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

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