scholarly journals The stability in $L\sb p$ and $W\sp 1\sb p$ of the $L\sb 2$-projection onto finite element function spaces

1987 ◽  
Vol 48 (178) ◽  
pp. 521-521 ◽  
Author(s):  
M. Crouzeix ◽  
V. Thom{ée
1974 ◽  
Vol 23 (3) ◽  
pp. 193-197 ◽  
Author(s):  
Jim Douglas ◽  
Todd Dupont ◽  
Lars Wahlbin

2004 ◽  
Vol 2004 (5) ◽  
pp. 217-238 ◽  
Author(s):  
Nikolai Yu. Bakaev

We present some resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces, for which the first space in a pair is endowed with stronger norm. In this work we deal with estimates in (Lebesgue, Lebesgue), (Hölder, Lebesgue), and (Hölder, Hölder) pairs of norms. In particular, our results are useful for the stability and error analysis of semidiscrete and fully discrete approximations to parabolic partial differential problems with rough and distribution-valued data.


2021 ◽  
Vol 11 (9) ◽  
pp. 3770
Author(s):  
Monica Tatarciuc ◽  
George Alexandru Maftei ◽  
Anca Vitalariu ◽  
Ionut Luchian ◽  
Ioana Martu ◽  
...  

Inlay-retained dental bridges can be a viable minimally invasive alternative when patients reject the idea of implant therapy or conventional retained full-coverage fixed dental prostheses, which require more tooth preparation. Inlay-retained dental bridges are indicated in patients with good oral hygiene, low susceptibility to caries, and a minimum coronal tooth height of 5 mm. The present study aims to evaluate, through the finite element method (FEM), the stability of these types of dental bridges and the stresses on the supporting teeth, under the action of masticatory forces. The analysis revealed the distribution of the load on the bridge elements and on the retainers, highlighting the areas of maximum pressure. The results of our study demonstrate that the stress determined by the loading force cannot cause damage to the prosthetic device or to abutment teeth. Thus, it can be considered an optimal economical solution for treating class III Kennedy edentation in young patients or as a provisional pre-implant rehabilitation option. However, special attention must be paid to its design, especially in the connection area between the bridge elements, because the connectors and the retainers represent the weakest parts.


2021 ◽  
Vol 8 (1) ◽  
pp. 130-136
Author(s):  
Roberto Spagnuolo

Abstract The stability check of masonry structures is a debated problem in Italy that poses serious problems for its extensive use. Indeed, the danger of out of plane collapse of masonry walls, which is one of the more challenging to evaluate, is traditionally addressed not using finite element models (FEM). The power of FEM is not properly used and some simplified method are preferred. In this paper the use of the thrust surface is suggested. This concept allows to to evaluate the eccentricity of the membrane stresses using the FEM method. For this purpose a sophisticated, layered, finite element with a no-tension material is used. To model a no-tension material we used the smeared crack method as it is not mesh-dependent and it is well known since the early ’80 in an ASCE Report [1]. The described element has been implemented by the author in the program Nòlian by Softing.


2019 ◽  
Vol 19 (10) ◽  
pp. 2079-2095 ◽  
Author(s):  
Michele Perrotti ◽  
Piernicola Lollino ◽  
Nunzio Luciano Fazio ◽  
Mario Parise

Abstract. The stability of man-made underground cavities in soft rocks interacting with overlying structures and infrastructures represents a challenging problem to be faced. Based upon the results of a large number of parametric two-dimensional (2-D) finite-element analyses of ideal cases of underground cavities, accounting for the variability both cave geometrical features and rock mechanical properties, specific charts have been recently proposed in the literature to assess at a preliminary stage the stability of the cavities. The purpose of the present paper is to validate the efficacy of the stability charts through the application to several case studies of underground cavities, considering both quarries collapsed in the past and quarries still stable. The stability graphs proposed by Perrotti et al. (2018) can be useful to evaluate, in a preliminary way, a safety margin for cavities that have not reached failure and to detect indications of predisposition to local or general instability phenomena. Alternatively, for sinkholes that already occurred, the graphs may be useful in identifying the conditions that led to the collapse, highlighting the importance of some structural elements (as pillars and internal walls) on the overall stability of the quarry system.


2016 ◽  
Vol 08 (07) ◽  
pp. 1640009 ◽  
Author(s):  
Fengfeng Li ◽  
Liwu Liu ◽  
Xin Lan ◽  
Tong Wang ◽  
Xiangyu Li ◽  
...  

With large spatial deployable antennas used more widely, the stability of deployable antennas is attracting more attention. The form of the support structure is an important factor of the antenna’s natural frequency, which is essential to study to prevent the resonance. The deployable truss structures based on shape memory polymer composites (SMPCs) have made themselves feasible for their unique properties such as highly reliable, low-cost, light weight, and self-deployment without complex mechanical devices compared with conventional deployable masts. This study offers deliverables as follows: an establishment of three-longeron beam and three-longeron truss finite element models by using ABAQUS; calculation of natural frequencies and vibration modes; parameter studies for influence on their dynamic properties; manufacture of a three-longeron truss based on SMPC, and modal test of the three-longeron truss. The results show that modal test and finite element simulation fit well.


2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.


2011 ◽  
Vol 03 (01n02) ◽  
pp. 91-107 ◽  
Author(s):  
JÜRGEN LEOPOLD ◽  
KATRIN HELLER ◽  
ARNDT MEYER ◽  
REINER WOHLGEMUTH

The stability of coating-substrate systems influences the chip formation and the surface integrity of the new generated workpiece surface, too. Using finite element (FE) simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in μm-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an advanced adaptive finite element (AAFEM) software has been developed and used for the simulation.


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