Weak Formulation of Finite Element Method for Nonlocal Beams Using Additional Boundary Conditions

2011 ◽  
Vol 8 (11) ◽  
pp. 2173-2180 ◽  
Author(s):  
Mustafa Özgür Yayli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Weak Formulation ◽  
Additional Boundary Conditions ◽  
Element Method

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

2021 ◽  
pp. 244-256
Author(s):  
Виктор Григорьевич Чеверев ◽  
Евгений Викторович Сафронов ◽  
Алексей Александрович Коротков ◽  
Александр Сергеевич Чернятин
Keyword(s):  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Soil Freezing ◽  
The Finite Element Method ◽  
Freezing Front ◽  
Element Method

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

scholarly journals Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

1999 ◽  
Vol 21 (2) ◽  
pp. 116-128
Author(s):  
Pham Thi Toan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Multilayered Composite ◽  
Internal Forces ◽  
External Loads ◽  
Element Method ◽  
Composite Cylindrical Shells

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

Strains distribution in biaxial Ge/CdSe nanowire analyzed by a new finite element method based on boundary conditions

2013 ◽  
Author(s):  
Dong Wang ◽  
Chunrui Wang ◽  
Yao Zhang ◽  
Shasha Zhang ◽  
Xiaofeng Xu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Element Method

The Inverse Least-Squares Finite Element Method Applied to the Convection-Diffusion Equation

2009 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Heat Fluxes ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Current Formulation ◽  
Element Method

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in problems governed by the steady convection-diffusion equation will be presented. The method is capable of determining temperatures, and heat fluxes in location where such quantities are unknown provided such quantities are sufficiently over-specified in other locations. For the current formulation it is assumed the velocity field is known. The current formulation is unique in that it results in a sparse square system of equations even for partial differential equations that are not self-adjoint. Since this formulation always results in a symmetric positive-definite matrix, the solution can be found with standard sparse matrix solvers such as preconditioned conjugate gradient method. In addition, the formulation allows for equal order approximation of temperature and heat fluxes as it is not subject to the inf-sup condition. The formulation allow for a treatment of over-specified boundary conditions. Also, various forms of regularization can be naturally introduced within the formulation. Details of the discretization and sample results will be presented.

scholarly journals Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

2019 ◽  
Author(s):  
Liang Wang ◽  
Xue Zhang ◽  
Filippo Zaniboni ◽  
Eugenio Oñate ◽  
Stefano Tinti
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Element Formulation ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Landslide Modeling ◽  
Element Method

AbstractNotwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

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