Linear and non-linear deflection analysis of thick rectangular plates—I. theoretical derivation

Non-linear analysis of thick rectangular plates has been conducted using general three-dimensional equations; simplifications are made only for small rotations. The governing dimensionless partial differential equations in terms of the displacement components U, V, and W were derived. Non-linear analysis using the von Kármán equations can be considered as a particular case when the plate thickness is very small. Finite difference techniques were used to transform the partial differential equations into an algebraic system of equations to yield the solutions. The successive approximation technique is used to pursue the convergence of the dimensionless non-linear deflection of thick plates, using an under-relaxation factor γ with the linear deflection results as the first guess for the analysis.     

Linear stability analysis in fluid-structure interaction with transpiration. Part II: Numerical analysis and applications

This paper constitutes the numerical counterpart of the mathematical framework introduced in Part I. We address the problem of flutter analysis of a coupled fluid-structure system involving an incompressible Newtonian fluid and a reduced structure. We use the Linearization Principle approach developed in Part I, particularly suited for fluid-structure problems involving moving boundaries. Thus, the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity. This eigenproblem involves the linearized incompressible Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration interface conditions. The eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized Cayley transform and an implicit restarted Arnoldi method. Finally, we report three numerical experiments: a structure immersed in a fluid at rest, a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects. The numerical results are compared to former approaches and experimental data. The quality of these numerical results is very satisfactory and promising.     

Load deflection analysis of rectangular graphene diaphragm for MEMS intracranial pressure sensor applications

Microsystem Technologies - There is a need to establish an ultra-small micro pressure sensors in dynamic performance for intracranial monitoring which can reduce the risk of inflammation and...     

On the design and analysis of simply supported and clamped thick rectangular plates

The finite difference method, although well known as an efficient numerical method, was applied in the past, in the case of plate problems, only for the solution of thin plates. In the present study, the suitability of the method for problems involving thick plates is studied. The finite difference method as applied here is a modified finite difference approach to the ordinary finite difference method generally used for the solution of thin plate problems. Thin plates are treated as a particular case of the corresponding thick plates. The method is first applied to investigate the behaviour of clamped, square isotropic homogeneous thick plates. After the validity of the method is established, it is then extended to the solution of similar problems for simply supported square plates. Once the solution for a thick plate with a particular plate aspect ratio and boundary condition is obtained using a limited number of mesh sizes, a more refined solution to investigate the accuracy and convergence of the problem is then extended by providing more detailed functions satisfying the mesh sizes generated automatically by a computer program.

Whenever possible results of the present method are compared with existing solutions in the technical literature obtained by much more laborious numerical techniques, and close agreements are found. The submatrices involved in the formation of the finite difference equations from the governing differential equations are generated directly by the computer program. Simplicity in formulation and quick convergence are the obvious advantages of the method in comparison with other numerical methods requiring extensive computer facilities.     

An efficient computer program for the large deflection analysis of rectangular orthotropic plates

A computer program is presented for the static analysis of rectangular specially orthotropic plates undergoing large deflections. In-plane loads and lateral pressure are both catered for, together with various combinations of boundary conditions. However, a restriction is that there must be symmetry about both plate axes. The plate can have an initial geometrical imperfection, which is represented by a double Fourier series with the same terms as that used for the lateral displacement. By specifying in the input data suitable values for the coefficients in the imperfection series, the effect of relatively complicated initial shapes can be examined. The program is called ELDAROP, a FORTRAN listing of which is given in Appendix A. Appendix B contains a listing of the associated subroutine STRRES, which calculates stress resultants. The analysis is based on equations derived in a recent paper (Comput. Struct. 26, 871–884, 1987), in which it was demonstrated that ELDAROP appears to be both accurate, and extremely rapid in its operation. Appendices C-E give examples of the simple arrangement of input data and output.     

Bending analysis of rectangular moderately thick plates using spline finite element method

A bending analysis of rectangular, moderately thick plates with general boundary conditions is presented using the spline element method. The cubic B spline interpolate functions are used to construct the field function of generalized displacements w, φ_itxand φ_ity. The spline finite element equations are derived based on the potential energy principle. For simplicity, the boundary conditions, which consist of three local spline points, are amended to fit specified boundary conditions. The shear effect is considered in the formulations. A number of numerical examples are described for rectangular, moderately thick plates. Since the cubic B spline interpolate functions have sufficient continuity and are piecewise polynomial, so the present numerical solutions show not only that the method gives accurate results, but also that the unified solutions of thick and thin plates can be directly obtained; the trouble with the so-called shear locking phenomenon does not occur here.     

A new hybrid F.E. model for arbitrarily curved beam—I. Linear analysis

The finite element analysis of curved structures (arches, shells) has always presented great difficulty. In fact, in recent years, many researchers have soundly investigated the meaning of the poor convergence rate and the locking phenomena exhibited by the traditional displacement approaches. Nevertheless, selective or reduced integration methods and multi-field variational formulations have proved capable of overcoming these difficulties. In this paper the problem is discussed once more, starting from the basic idea that for a rod it is always possible to set up internal force fields, which pointwise satisfy exactly the indefinite equilibrium equations. The use of a finite set of stress parameters (for instance, the stress resultant components) to describe the internal force is well documented in the technical literature. Unfortunately these studies are all focussed on a particular arch geometry, without a systematic generalization.

This limitation can be overcome through the substitution of the axis line by a cubic B-spline approximated one. The proposed method allows an easy and systematic generation of the mentioned equilibrated stress resultant field. In this way it is possible to compute exactly (apart from the numerical integration error) the flexibility matrix, or according to the classical works of Pian, the curved beam stiffness matrix directly.

The paper ends with some technically relevant numerical experiments, which illustrate the good performances of the proposed model, independently of the shape and aspect ratio of the arch, even with one element.     

Modeling multibody systems with uncertainties. Part II: Numerical applications

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects”.In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set.The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties.     

Free vibration analysis and optimisation of axisymmetric plates and shells—II. Shape optimisation

The second part of this paper is concerned with the structural shape optimisation of vibrating axisymmetric shells. Natural frequencies and mode shapes are determined using curved, variable thickness, Mindlin-Reissner FEs introduced and benchmarked in the first part of the paper. The whole shape optimisation process is carried out by integrating FE analysis, cubic spline shape and thickness definitions, sensitivity analysis and mathematical programming. The semi-analytical method is used to determine the sensitivities of the objective function and constraints to changes in the design variables. Several examples are considered to illustrate and highlight various features of the optimisation, including various plates, a conical shell, a branched shell, and a church bell.     

Laminar flow in rectangular channels. Part I: Entry analysis. Part II: Numerical solution for a square channel?

Laminar incompressible flow in rectangular channels is considered. In Part I, the entry region is evaluated by a boundary layer/potential core analysis. It is shown that the three-dimensional displacement induced potential flow can be described with a pair of two-dimensional potential functions. Second-order boundary layer solutions, with and without surface mass transfer, are determined; an interesting secondary flow reversal is predicted. In Part II, numerical solutions are obtained for the viscous channel equations, which are derived from the asymptotic theory of Part I. A two stream function, velocity, vorticity system, independent of the Reynolds Number, is solved with a combined iterative ADI/point-relaxation numerical procedure. A single calculation applied for all Reynolds numbers, which appears only in the coordinate scaling. The axial flow behavior of Parts I and II are in good agreement in the asymptotic entry region where both analysis apply. Secondary flow reversal is calculated; however, the grid is too crude for quantitative comparisons. Numerical solutions are obtained until fully developed conditions are achieved. Agreement with experimental data is good.     

CCITT X.500 Directories — principles and applications

Directories can be used as a service to provide human users or application processes with on-line access to what telecommunication services exist, where they reside, and how the correspondents might be accessed and addressed in a distributed environment. They will provide for the mapping of user-friendly recipient names to addresses in a consistent and standardized manner. In fact, any application which interacts with named objects in a distributed environment can benefit from the use of directory services.     

Nonlinear analysis of reinforced concrete hyperboloid cooling towers—II. Parametric study and results

In this second and final part of this series of papers the details of parametric studies conducted to assess the influence of various geometric and material parameters on the load-displacement response of three reinforced concrete hyperboloid cooling towers are presented. The material model adopted for the nonlinear finite element analysis is described in part I of this paper.     

Hybrid strain based three node flat triangular shell elements—II. Numerical investigation of nonlinear problems

In a companion paper [M. L. Liu and C. W. S. To, Comput. Struct. 54, 1031–1056 (1995)] theories and incremental formulation of nonlinear shell structures discretized by the finite element method are discussed. The updated Lagrangian formulation and the incremental Hellinger-Reissner variational principle are adopted. The independently assumed fields employed are the incremental displacements and incremental strains. Based on the theory and incremental formulation explicit element stiffness and mass matrices of three node flat triangular shell finite elements are derived. In the present paper the derived element matrices are applied to nine examples. The latter include static and dynamic response analysis of shell structures with geometrical, material, and geometrical and material nonlinearities. The formulation adopted and element matrices derived are found to be accurate, flexible and applicable to various types of shell structures with geometrical and material nonlinearities.     

Computation and solution procedures for non-linear analysis by combined finite element — finite difference methods

This paper begins with the basic principle of virtual work and derives expressions for the pseudo forces and contributions to the tangent stiffness matrix for geometric and material nonlinearities. For this formulation a computional procedure is presented which evaluates the effects of nonlinearities through the use of finite difference expressions. This computational procedure is an order of magnitude faster than reported by other researchers and permits the solution for complex nonlinear behavior in reasonable times on the computer. Examples are presented for the large elastic-plastic deflections of shells of revolution under both static and dynamic loading and computer times are reported.     

Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications

Summary In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional contact formulation is fully developed on the continuum setting and then a spatial (Galerkin projection) and temporal (time-stepping algorithm) discretization is applied. A contact pressure and temperature dependent thermal contact model has been used. A fractional step method arising from an operator split of the governing equations has been used to solve the coupled nonlinear system of equations, leading to a staggered solution algorithm. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of coupled thermomechanical frictional contact problems.     

Computer-aided optimal design of a polar-based template digitizer-NC contouring system—II. Dynamic analysis

This paper presents the computer-aided optimal design of a template digitizer-NC contouring system which utilizes a set of polar coordinates. The system can operate both as a copying machine or as a numerical control (NC) machine. Part I of the paper describes the proposed system and its salient features. It also analyzes the contouring error due to the incremental approximation of the contour. This error is dependent on the relative location of the contour pole from the machine pole. An objective function relating the area error to the position of the contour is derived and an optimization procedure to minimize this error is outlined. Test results of an attempt to locate the poles of three test contours for minimum error are then presented.     

A refined analysis of laminated plates by finite element displacement methods—II. Vibration and stability

A refined anisotropic laminated plate bending analysis is presented in a companion paper to the present work (Computers and Structures 26, 907–914, 1987). In the present paper, a refined transverse vibration and buckling analysis based on the same local model is presented. The numerical examples presented are compared with analytical solutions and classical plate theory and it is demonstrated that the present model predicts a realistic laminate global response.     

II. Supporting models and applications

Baaed on TOC (Task Operating Characteristic) and ROC (Resource Operating Characteristic) curves (Braswell 1971), P(t) and R(t), a family of feasible curves are experimentally selected with parameter specifications for a and S. Additional models are developed for activity progress and resource utilization monitoring and control. A resource allocation method is developed and a Best 1'ath (JJP) strategy is presented to reprogramme progress of assignments and rates of resource expending. Task Progress (TP) and Rosource Depletion (RD) models are developed. Examples, and figures illustrate applications.