scholarly journals Finite elements for problems of the elasticity theory with the discontinuous stress approximation

2020 ◽  
Vol 224 ◽  
pp. 02012
Author(s):  
A Lukashevich ◽  
N Lukashevich ◽  
E Kobelev
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Approximation Schemes ◽  
Stress Fields ◽  
Penalty Function Method ◽  
Finite Element Models ◽  
Equilibrium Equations ◽  
Additional Energy ◽  
Calculation Results ◽  
Displacement Based

The paper deals with the development of the finite element models on the basis of stress approximation. At present, the displacementbased finite element method is mainly used for engineering calculations. Finite element formulations in stresses are not so widely spread, but in some cases these formulations can be more effective in particular with respect to the calculating stresses and also obtaining a two-sided estimate of the exact solution of the problem. The finite element models based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations are considered. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. The necessary matrix relations for rectangular and triangular finite elements are obtained. The effectiveness of the developed models is illustrated by numerical studies. The calculation results were compared with the solution on the FEM in displacements, as well as with the results obtained using other schemes of approximating the stresses in the finite element. It is shown that the model of discontinuous stress approximations gives the bottom convergence of the solution, both in stresses and in displacements. At the same time, the accuracy on the stresses here is much higher than in the displacement-based FEM or when using conventional stress approximation schemes.

Modelling of Rotating Twisted Blades as 1D Continuum

2016 ◽  
Vol 821 ◽  
pp. 183-190
Author(s):  
Jan Brůha ◽  
Drahomír Rychecký
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Beam Theory ◽  
Parameter Tuning ◽  
Finite Element Models ◽  
Cross Sectional ◽  
One Dimensional ◽  
Rayleigh Beam ◽  
Twisted Blade ◽  
Sectional Parameters

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

scholarly journals Hierarchical Beam Finite Elements Based Upon a Variables Separation Method

2016 ◽  
Vol 08 (02) ◽  
pp. 1650026 ◽  
Author(s):  
Gaetano Giunta ◽  
Salim Belouettar ◽  
Olivier Polit ◽  
Laurent Gallimard ◽  
Philippe Vidal ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Three Dimensional ◽  
Finite Element Solution ◽  
Stress Fields ◽  
Element Solution ◽  
One Dimensional ◽  
Kinematic Approximation ◽  
The Cross

A family of hierarchical one-dimensional beam finite elements developed within a variables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equivalent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.

scholarly journals REGULARITIES OF THE LINING STRESS-STRAIN STATE DURING OF THE PYLON METRO STATION CONSTRUCTION

2021 ◽  
pp. 19-27
Author(s):  
D. O. BANNIKOV ◽  
V. P. KUPRII ◽  
D. YU. VOTCHENKO
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Finite Elements ◽  
Strain State ◽  
Finite Element Models ◽  
Bending Moments ◽  
Stress Strain ◽  
Normal Forces ◽  
Stress Strain State ◽  
Station Structure

Purpose. Perform numerical analysis of the station structure. Take into account in the process of mathematical modeling the process of construction of station tunnels of a three-vaulted station. Obtain the regularities of the stress-strain state of the linings, which is influenced by the processes of soil excavation and lining construction. Methodology. To achieve this goal, a series of numerical calculations of models of the deep contour interval metro pylon station was performed. Three finite-element models have been developed, which reflect the stages of construction of a three-vaulted pylon station. Numerical analysis was performed on the basis of the finite element method, implemented in the calculation complex Lira for Windows. Modeling of the stress-strain state of the station tunnel linings and the soil massif was performed using rectangular, universal quadrangular and triangular finite elements, which take into account the special properties of the soil massif. Station tunnel linings are modeled by means of rod finite elements. Findings. Isofields of the stress-strain state in finite-element models reflecting the stages of construction are obtained. The vertical displacements and horizontal stresses that are characteristic of a three-vaulted pylon station are analyzed. The analysis of horizontal stresses proved that at the stage of opening of the middle tunnel the scheme of pylon operation is rather disadvantageous. The analysis of bending moments and normal forces was also carried out and the asymmetry of their distribution was noted. Originality. Based on the obtained patterns of distribution of stress-strain state and force factors, it is proved that numerical analysis of the station structure during construction is necessary to take measures to prevent or reduce deformation of frames that are in unfavorable conditions. Practical value. In the course of research, the regularities of changes in stresses, displacements, bending moments and normal forces in the models of the pylon station, which reflect the sequence of its construction, were obtained.

Research on the Influence of the Stiffening Plates on the Stress of Hold Hoop of Bent Cap

2019 ◽  
Vol 815 ◽  
pp. 223-228
Author(s):  
Qin Tian ◽  
Cheng Hao Hang ◽  
Yun Peng Zou ◽  
Zi Xin Wan
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Stress Concentration ◽  
Structural Parameters ◽  
Great Influence ◽  
Finite Element Models ◽  
Finite Element Software ◽  
Bridge Steel ◽  
Calculation Results ◽  
Shell Finite Element

In order to improve the mechanical behaviour of bridge steel hoops, the plate shell finite element models of several steel hoops were established by using the general finite element software ABAQUS. Through changing the structural parameters of the stiffening plates, the influence of the stiffening plates on the mechanical properties of the steel hoops was explored. The calculation results show that the stress distribution at both ends of the steel hoop is uneven and there is a phenomenon of stress concentration. The spacing of stiffening plates has great influence on the mechanical properties of steel hoop. Some measures to improve the mechanical properties of steel hoop are given.

Fatigue Life Calculation of the in-Service Dented Pipeline

2011 ◽  
Vol 467-469 ◽  
pp. 1327-1332 ◽  
Author(s):  
Wu Ying ◽  
Peng Zhang ◽  
Wu Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fatigue Life ◽  
Pressure Variation ◽  
Finite Element Models ◽  
Test Results ◽  
Peak Period ◽  
Factors Affecting ◽  
Life Model ◽  
Calculation Results

Dent is one of the important factors affecting pipeline fatigue life, and it will greatly reduce the fatigue life of the pipeline in service. Based on a large number of foreign dented pipeline fatigue test results and fatigue life model, for the typical dent defect, using finite element method, various parameters are changed and finite element models are obtained under different conditions. According to many calculation results, a key ratio of peak period stress and pipeline pressure variation are obtained, which are substituted to the fatigue life model and the example are calculated.

Evaluating the Effect of Nozzle Weld Stiffness When Using Shell Finite Element Models for ASME Code Evaluations

2012 ◽  
Author(s):  
Bryan Dunlap ◽  
Hassan Ziada ◽  
John Julyk
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Shell Element ◽  
Finite Element Models ◽  
Shell Elements ◽  
Asme Code ◽  
Section Viii ◽  
Shell Finite Element ◽  
Code Compliance ◽  
Division 2

Typically the use of SHELL finite elements to model nozzle/vessel interfaces will not include details of the weld at the interface. The omission of the weld details from SHELL element models is due to the difficulty in implementing such details and the assumption that additional interface stiffness due to the weld will have a negligible effect on results at locations of interest for Code evaluation. This study will demonstrate a proposed method for modeling weld details with SHELL elements and then evaluate the magnitude of the weld stiffness effect on results and Code compliance. The method of modeling the weld details with SHELL elements used in this study will follow the guidance provided by ASME BPVC Section VIII, Division 2, Annex 5.A [2] for such interfaces. Models of nozzle/vessel interfaces will be shown comparing results of SOLID element models with and without the weld detail, and then SHELL element models both with and without the weld detail. The results from these models will be evaluated and recommendations for future modeling and evaluation of nozzle/shell interfaces with SHELL elements will be offered.

scholarly journals Development of Practical Finite Element Models for Collapse of Reinforced Concrete Structures and Experimental Validation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Mario Bermejo ◽  
Anastasio P. Santos ◽  
José M. Goicolea
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Finite Elements ◽  
Finite Element Model ◽  
Computational Cost ◽  
Concrete Structures ◽  
Element Model ◽  
Reinforced Concrete Structures ◽  
Finite Element Models ◽  
Explicit Finite Element

This paper describes two practical methodologies for modeling the collapse of reinforced concrete structures. They are validated with a real scale test of a two-floor structure which loses a bearing column. The objective is to achieve accurate simulations of collapse phenomena with moderate computational cost. Explicit finite element models are used with Lagrangian meshes, modeling concrete, and steel in a segregated manner. The first model uses 3D continuum finite elements for concrete and beams for steel bars, connected for displacement compatibility using a penalty method. The second model uses structural finite elements, shells for concrete, and beams for steel, connected in common nodes with an eccentricity formulation. Both are capable of simulating correctly the global behavior of the structural collapse. The continuum finite element model is more accurate for interpreting local failure but has an excessive computational cost for a complete building. The structural finite element model proposed has a moderate computational cost, yields sufficiently accurate results, and as a result is the recommended methodology.

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