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.

Large Nonlinear Random Responses of Spatially Non-Homogeneous Stochastic Shell Structures

2006 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Random Excitation ◽  
Shell Structures ◽  
Response Analysis ◽  
Hybrid Strain ◽  
Central Difference ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Random Disturbances ◽  
Excitation Processes

This paper is concerned with large nonlinear random response analysis of spatially non-homogeneous stochastic shell structures under transient excitations. The latter are treated as nonstationary random excitation processes. The emphases are on (i) spatially non-homogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, and (iii) intensive nonstationary random disturbances. 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 nonstationary random nonlinear responses are evaluated by a procedure that consists of the stochastic central difference method, time co-ordinate transformation, and modified adaptive time scheme. Computationally, the procedure is very efficient compared with those entirely and partially based on Monte Carlo simulation, and is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method.

Nonlinear Random Responses of Shell Structures With Spatial Uncertainties

2002 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Mass Matrix ◽  
Spatial Uncertainty ◽  
Shell Structures ◽  
Time Step ◽  
Central Difference ◽  
Approximation Techniques ◽  
Element Method

A novel procedure for large deformation nonstationary random response computation of shell structures with spatial uncertainty is presented. The procedure is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element method and probabilistic finite element method, for systems with spatial uncertainties. In addition, the procedure has several important and excellent features. Chief among these are: (a) ability to deal with large deformation problems of finite strain and finite rotation; (b) application of explicit linear and nonlinear element stiffness matrices, mass matrix, and load vectors reduces computation time drastically; (c) application of the averaged deterministic central difference scheme for the updating of co-ordinates and element matrices at every time step makes it extremely efficient compared with those employing the Monte Carlo simulation and the conventional central difference algorithm; and (d) application of the time co-ordinate transformation enables one to study highly stiff structural systems.

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.

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.

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.

Non-Conservative and Conservative Loads in Geometrically Nonlinear Shells

2003 ◽  
Author(s):  
Cho W. S. To ◽  
Meilan L. Liu
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Small Strain ◽  
Shell Structures ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Hybrid Strain ◽  
Shell Elements ◽  
Updated Lagrangian Formulation ◽  
Updated Lagrangian

Responses of geometrically nonlinear shell structures under combined conservative and non-conservative loads are investigated and presented in this paper. The shell structures are discretized by the finite element method and represented by the hybrid strain based three node flat triangular shell elements that were developed previously by the authors. The updated Lagrangian formulation and the incremental Hellinger-Reissner variational principle are employed. Features such as large or small strain deformation, finite rotation, updated thickness so as to account for the “thinning effect” due to large strain deformation, and inclusion or exclusion of the mid-surface director field are incorporated in the finite element formulation. Representative results of two examples are included to demonstrate the capability, accuracy and efficiency of the computational strategy proposed.

Responses of Stochastic Shell Structures to Non-Gaussian Random Excitations

2008 ◽  
Author(s):  
Cho W. S. To
Keyword(s):  
Finite Elements ◽  
Acoustic Radiation ◽  
Random Excitation ◽  
Ease Of Use ◽  
Shell Structures ◽  
Central Difference ◽  
Spherical Cap ◽  
Relative Ease ◽  
Central Difference Method ◽  
Non Gaussian

An approach dealing with the responses of and acoustic radiation from temporally and spatially stochastic shell structures to non-Gaussian random excitations is presented in this paper. It employs the stochastic central difference method developed earlier by the author and his associate. The emphasis of the presentation is, however, on the responses of stochastic shell structures with large spatial variations and under non-Gaussian nonstationary random excitations. The shell structures are discretized by the mixed formulation, lower order triangular shell finite elements developed by the author and his associate in 1994. As a demonstration of the relative ease of use of the approach, computed results for a temporally and spatially stochastic, clamped spherical cap subjected to a central point force treated as a non-Gaussian nonstationary random excitation are included. It is concluded that a simple and relatively very efficient approach is available for analysis of responses of temporally and spatially stochastic shell structures perturbed by non-Gaussian nonstationary random excitations.

scholarly journals A Novel Particle-Based Approach for Modeling a Wet Vertical Stirred Media Mill

Minerals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 55
Author(s):  
Simon Larsson ◽  
Juan Manuel Rodríguez Prieto ◽  
Hannu Heiskari ◽  
Pär Jonsén
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Grinding Fluid ◽  
Novel Approach ◽  
Grinding Media ◽  
Interparticle Contacts ◽  
Mineral Slurry ◽  
Stirred Media Mill ◽  
Element Method

Modeling of wet stirred media mill processes is challenging since it requires the simultaneous modeling of the complex multiphysics in the interactions between grinding media, the moving internal agitator elements, and the grinding fluid. In the present study, a multiphysics model of an HIG5 pilot vertical stirred media mill with a nominal power of 7.5 kW is developed. The model is based on a particle-based coupled solver approach, where the grinding fluid is modeled with the particle finite element method (PFEM), the grinding media are modeled with the discrete element method (DEM), and the mill structure is modeled with the finite element method (FEM). The interactions between the different constituents are treated by loose (or weak) two-way couplings between the PFEM, DEM, and FEM models. Both water and a mineral slurry are used as grinding fluids, and they are modeled as Newtonian and non-Newtonian fluids, respectively. In the present work, a novel approach for transferring forces between grinding fluid and grinding media based on the Reynolds number is implemented. This force transfer is realized by specifying the drag coefficient as a function of the Reynolds number. The stirred media mill model is used to predict the mill power consumption, dynamics of both grinding fluid and grinding media, interparticle contacts of the grinding media, and the wear development on the mill structure. The numerical results obtained within the present study show good agreement with experimental measurements.

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