scholarly journals Finite Elements for the One Variable Version of Mindlin-Reissner Plate

2020 ◽  
Vol 17 (6) ◽  
Author(s):  
Kamal Hassan ◽  
Ehab Ali ◽  
Mohammad Tawfik
Author(s):  
Rakesh K. Kapania ◽  
Sungho Park

Abstract The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, the Hermite, the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various system parameters can be obtained.


2015 ◽  
Vol 8 (4) ◽  
pp. 491-506
Author(s):  
J. A. DE CARVALHO NETO ◽  
L. A. C. M. VELOSO

AbstractThe knowledge on the active moving load of a bridge is crucial for the achievement of the information on the behavior of the structure, and thus foresee maintenance, repairs and better definition of the logistics of its active vehicles. This paper presents the development of the algorithms for the application of the Bridge-Weigh In Motion (B-WIM) method created by Moses for the weighing of trains during motion and also for the characterization of the rail traffic, allowing the obtainment of information like passage's train velocity and number and spacing of axles, eliminating the dynamic effect. There were implemented algorithms for the determination of the data referring to the geometry of the train and its loads, which were evaluated using a theoretical example, in which it was simulated the passage of the train over a bridge and the loads of its axles were determined with one hundred percent of precision. In addition, it was made a numerical example in finite elements of a reinforced concrete viaduct from the Carajás' Railroad, in which the developed system reached great results on the characterization and weighing of the locomotive when the constitutive equation of the Brazilian Standards was substituted by the one proposed by Collins and Mitchell.


2019 ◽  
Vol 91 ◽  
pp. 02013
Author(s):  
Vladimir Agapov

Urban development requires careful attitude to environment on the one hand and protection of the population from the natural phenomena on the other. To solve these problems, various building structures are used, in which slabs and shells of variable thickness find the wide application. In this work, the family of multilayered finite elements for the analysis of plates and shells of variable thickness is described. The family is based on the simplest flat triangular element of the Kirchhoff type. The lateral displacements in this element are approximated by an incomplete cubic polynomial. Such an element is unsuitable for practical use, but on its basis, improved elements of triangular and quadrilateral shape are built. Particular attention is paid to taking into account the variability of the cross-section. The results of the developed elements testing are presented, and the advantages of their use in the practice of designing and calculating the structures are shown.


2015 ◽  
Vol 5 (2) ◽  
pp. 43-50
Author(s):  
L. Kopenetz ◽  
A. Cătărig ◽  
Mihaela Teodora Ghemiş

Abstract In the case of light structures membrane type the form is confused with the structure and vice versa. Thus the analysis process, non-linear type, the one for form finding is also a means of optimizing these structures. To respect the natural principle of minimum it is advisable that the structure’s shape is similar to the minimum surface area. The numerical problem solving is based on using finite elements with constant strain of soap film. Based on these considerations, the paper presents aspects of determining the shape of the membrane structure using finite elements of soap film.


2021 ◽  
Vol 2 (4) ◽  
pp. 5034-5048
Author(s):  
Vladimir P. Agapov ◽  
Alexey Markovich

Urban development requires careful attitude to environment on the one hand and protection of the population from the natural phenomena on the other. To solve these problems, various building structures are used, in which slabs and shells of variable thickness find the wide application. In this work, the family of multilayered finite elements for the analysis of plates and shells of variable thickness is described. The family is based on the simplest flat triangular element of the Kirchhoff type. The lateral displacements in this element are approximated by an incomplete cubic polynomial. Such an element is unsuitable for practical use, but on its basis, improved elements of triangular and quadrilateral shape are built. Particular attention is paid to taking into account the variability of the cross-section. The results of the developed elements testing are presented, and the advantages of their use in the practice of designing and calculating the structures are shown.   El desarrollo urbano requiere una actitud cuidadosa con el medio ambiente, por un lado, y la protección de la población frente a los fenómenos naturales, por otro. Para resolver estos problemas, se utilizan diversas estructuras de edificios, en las que las placas y cáscaras de espesor variable encuentran una amplia aplicación. En este trabajo se describe la familia de elementos finitos multicapa para el análisis de placas y cáscaras de espesor variable. La familia se basa en el elemento triangular plano más simple del tipo Kirchhoff. Los desplazamientos laterales en este elemento se aproximan mediante un polinomio cúbico incompleto. Este elemento es inadecuado para su uso práctico, pero sobre su base se construyen elementos mejorados de forma triangular y cuadrilátera. Se presta especial atención a tener en cuenta la variabilidad de la sección transversal. Se presentan los resultados de las pruebas de los elementos desarrollados y se muestran las ventajas de su uso en la práctica del diseño y el cálculo de las estructuras.  


1991 ◽  
Vol 113 (4) ◽  
pp. 482-493 ◽  
Author(s):  
T. C. Gmu¨r ◽  
J. D. Rodrigues

This paper presents efficient C0-compatible finite elements for the modelling of rotor-bearing systems. The proposed linearly tapered elements, which have a variable number of nodal points, are simple and attractive from a cost viewpoint. They include the effects of translational and rotatory inertia, gyroscopic moments, internal viscous and hysteretic damping, shear deformations, and mass eccentricity. Developed from the weak formulation associated with the differential equations governing the transverse dynamic behavior of rotors, these elements show a convergence pattern similar to the one obtained with conventional C1-compatible shaft elements. Numerical examples are provided, which compare the proposed approach to the C1-formulation or to previously published results.


1994 ◽  
Vol 04 (06) ◽  
pp. 795-806 ◽  
Author(s):  
JAN H. BRANDTS

In this paper we present some results on the discretization by mixed finite elements of the Timoshenko beam, i.e. the one-dimensional Reissner-Mindlin plate bending problem. The results concern superconvergence. Superconvergence (of the displacement at nodal points and of the gradient at Gaussian points) for plate bending problems was considered before, but these earlier results degenerate for small values of the plate thickness d. Here, we prove superconvergence of the mixed finite element solutions to projections of the real solutions on the approximating spaces in the global H1(I)-norm uniform in d. These facts can be used to obtain asymptotically exact a posteriori error estimators, uniform in d, by means of an easy implementable and cheap post-processing. Numerical experiments illustrate the conclusions.


2021 ◽  
pp. 073168442110095
Author(s):  
Wenjiao Zhang ◽  
Shuyuan Zhao ◽  
Rujie Sun ◽  
Fabrizio Scarpa ◽  
Jinwu Wang

We propose in this work an innovative hybrid auxetic metamaterial with a centersymmetric unit cell and tessellation topology similar to the one provided by the missing rib configuration. The tessellation proposed is applied to different core unit cells (star shape, cross-chiral shape with same dimensions, and reentrant). The effects of the geometric parameters of the cells on the in-plane mechanical properties of this hybrid auxetic metamaterial system are investigated via finite elements (FEMs). Representative unit cells (RUCs) with optimal mechanical behaviors are identified; those configurations exhibit the larger negative Poisson’s ratios and enhanced specific moduli. Designs related to two groups of auxetic metastructures with cylindric and cubic shapes are then developed based on the optimized RUCs along x and y directions. The equivalent mechanical performance of these metastructures under internal pressure is evaluated from a numerical standpoint. Auxetic cylindrical metastructures can be tailored by adjusting the number of the optimized RUCs along the circumferential and longitudinal directions, together with the geometric parameters of the optimized RUC itself. These hybrid auxetic metamaterials and metastructures provide the potential for multifunctional applications in biomechanics, flexible electronics, and aerospace.


1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.


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