Geometrically Nonlinear Calculation of Trailing rod designs. Part 1. Calculation of flexible threads

10.12737/335 ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 7-17
Author(s):  
Андрей Свентиков
Keyword(s):  
Linear Model ◽  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Constant Load ◽  
Geometrically Nonlinear ◽  
Flexible Rods ◽  
Nonlinear Matrix ◽  
Current Value ◽  
Special Case ◽  
Matrix Calculation

Is treated geometrically nonlinear matrix calculation core construction with the use of flexible threads. The first part is devoted to the study the major calculation dependencies of flexible threads. It is established that the geometric nonlinearity of flexible rods depends on the cube of the ratio of the calculation in a zero-offsets end stabilize relations to its current value. Also found that the constructive nonlinearity is a special case of geometrical nonlinearity and depends on the degree of impact on the VDS of flexible thread load on its own weight. It is found that the preliminary adjustment of the length of flexible rods leads to the increase of the share of the stresses of constant load and, accordingly, to the approximation of the nature of the work of these elements into a linear model.

Geometrically nonlinear calculation of trailing rod designs. Part 2. Matrix calculation of trailing systems

10.12737/336 ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 18-27 ◽  
Author(s):  
Андрей Свентиков
Keyword(s):  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Geometrically Nonlinear ◽  
Matrix Algorithms ◽  
Nonlinear Matrix ◽  
Matrix Calculation ◽  
Good Agreement

Is treated geometrically nonlinear matrix calculation of core construction with the use of flexible threads. The second part of the article is devoted to the study of matrix algorithms nonlinear calculation of hanging systems. For the geometrically nonlinear calculation was applied the method of elastic solutions, and for the constructive nonlinear basis of the method of successive approximations. The proposed methods have been tested on the well-known plane examples of the calculation, as well as on the example of study of the spatial hanging rod cover. The results found on the proposed methods have shown good agreement with the corresponding data of other authors. Also it is established that the greatest imbalance nodes in the cantilevered system is observed in the nodes of a fle­xible bearing thread, as well as in the nodes of the greatest intensity of the load.

THE SUPPORT BONDS RIGIDITY INFLUENCES ON THE CARRYING CAPACITY REDUCTION OF THE SHALLOW SHELLS ON A RECTANGULAR PLAN

2020 ◽  
Vol 92 (6) ◽  
pp. 3-12
Author(s):  
A.G. KOLESNIKOV ◽  
Keyword(s):  
Variable Thickness ◽  
Carrying Capacity ◽  
Geometric Nonlinearity ◽  
Progressive Collapse ◽  
Geometrically Nonlinear ◽  
Loss Of Stability ◽  
Shallow Shells ◽  
Capacity Reduction ◽  
Internal Forces ◽  
Hinged Support

Geometric nonlinearity shallow shells on a square and rectangular plan with constant and variable thickness are considered. Loss of stability of a structure due to a decrease in the rigidity of one of the support (transition from fixed support to hinged support) is considered. The Bubnov-Galerkin method is used to solve differential equations of shallow geometrically nonlinear shells. The Vlasov's beam functions are used for approximating. The use of dimensionless quantities makes it possible to repeat the calculations and obtain similar dependences. The graphs are given that make it possible to assess the reduction in the critical load in the shell at each stage of reducing the rigidity of the support and to predict the further behavior of the structure. Regularities of changes in internal forces for various types of structure support are shown. Conclusions are made about the necessary design solutions to prevent the progressive collapse of the shell due to a decrease in the rigidity of one of the supports.

scholarly journals Loglinear Model Formation using Hierachial Backward Method

2020 ◽  
Vol 2 (1) ◽  
pp. 28-36
Author(s):  
Siti Fatimah Sihotang ◽  
Zuhri
Keyword(s):  
Linear Model ◽  
Good Method ◽  
General Linear Model ◽  
Loglinear Model ◽  
Complete Model ◽  
The Third ◽  
Several Variables ◽  
Model Formation ◽  
Special Case ◽  
Categorical Scale

The loglinear model is a special case of a general linear model for poissondistributed data. The loglinear model is also a number of models in statistics that are used todetermine dependencies between several variables on a categorical scale. The number ofvariables discussed in this study were three variables. After the variables are investigated,the formation of the loglinear model becomes important because not all the modelinteraction factors that exist in the complete model become significant in the resultingmodel. The formation of the loglinear model in this study uses the Backward Hierarchicalmethod. This research makes loglinear modeling to get the model using the HierarchicalBackward method to choose a good method in making models with existing examples.From the challenging examples that have been done, it is known that the HierarchicalReverse method can model the third iteration or scroll. Then, also use better assessmentmethods about faster workmanship and computer-sponsored assessments that are used moreefficiently through compatibility testing for each model made

Application of the Nonlinear Model of a Beam for Investigation of Interlaminar Fracture Toughness of Layered Composite

2015 ◽  
Vol 665 ◽  
pp. 273-276 ◽  
Author(s):  
Vitalijs Pavelko
Keyword(s):  
Fracture Toughness ◽  
Nonlinear Model ◽  
Geometrical Nonlinearity ◽  
Local Effect ◽  
Layered Composite ◽  
Flexible Beam ◽  
Geometrically Nonlinear ◽  
Interlaminar Fracture Toughness ◽  
Linear Solution ◽  
Interlaminar Fracture

Earlier presented the geometrically nonlinear model of a flexible beam (cylindrical bending of a plate) was used for analysis of post-buckling behavior of the layered composite with delamination at compression. In this paper the model is used for more details nonlinear analysis of double cantilever beam (DCB) that used in standard test for determination of the interlaminar fracture toughness composites with delamination-type damage. The main advantage of the model is a precise description of the curved axis of the beam (plate) without linearization or other higher order approximations. The exact solution of bending differential equation finally can be expressed in terms of the incomplete elliptic integrals of the first and second kind. The model describes only geometrically nonlinear effect of DCB arms bending (global effect) and should be combined with the procedure of effective delamination extension to correct DCB arms rotation at delamination front (local effect). First of all the nonlinear model can serve as a tool to estimate the possible error due the geometrical nonlinearity in comparison with linear solution. On the other hand, this model can be effectively used to determine interlaminar fracture toughness using DCB samples at large deflections. Validation of the model is made using data of standard tests of glass/epoxy DCB samples.

Convex integration solutions for the geometrically nonlinear two-well problem with higher Sobolev regularity

2020 ◽  
Vol 30 (03) ◽  
pp. 611-651
Author(s):  
Francesco Della Porta ◽  
Angkana Rüland
Keyword(s):  
Dirichlet Problem ◽  
Boundary Conditions ◽  
Geometrically Nonlinear ◽  
Selection Mechanism ◽  
Matrix Space ◽  
Sobolev Regularity ◽  
Convex Integration ◽  
Nonlinear Matrix ◽  
Deformation Gradients ◽  
Higher Sobolev Regularity

In this paper, we discuss higher Sobolev regularity of convex integration solutions for the geometrically nonlinear two-well problem. More precisely, we construct solutions to the differential inclusion [Formula: see text] subject to suitable affine boundary conditions for [Formula: see text] with [Formula: see text] such that the associated deformation gradients [Formula: see text] enjoy higher Sobolev regularity. This provides the first result in the modelling of phase transformations in shape-memory alloys where [Formula: see text], and where the energy minimisers constructed by convex integration satisfy higher Sobolev regularity. We show that in spite of additional difficulties arising from the treatment of the nonlinear matrix space geometry, it is possible to deal with the geometrically nonlinear two-well problem within the framework outlined in [A. Rüland, C. Zillinger and B. Zwicknagl, Higher Sobolev regularity of convex integration solutions in elasticity: The Dirichlet problem with affine data in int[Formula: see text], SIAM J. Math. Anal. 50 (2018) 3791–3841]. Physically, our investigation of convex integration solutions at higher Sobolev regularity is motivated by viewing regularity as a possible selection mechanism of microstructures.

scholarly journals GEOMETRICAL NONLINEARITY ANALYSIS OF THE STEEL NETWORK ARCH BRIDGES / PLIENINŲ TINKLINIŲ ARKINIŲ TILTŲ GEOMETRINIO NETIESIŠKUMO VERTINIMAS

2016 ◽  
Vol 8 (5) ◽  
pp. 490-494
Author(s):  
Sigutė Žilėnaitė
Keyword(s):  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Compressive Force ◽  
Work Conditions ◽  
Geometrical Factor ◽  
Principal Behavior ◽  
New Construction ◽  
Arch Bridges ◽  
The Individual ◽  
The City

Arch bridges are one of the popular, oldest and graceful bridges which are being built in zones of the city and out of the city. However arches becomes especially sensitive to their buckling response due to dominated compressive force in the arch. In order to ensure stability conditions of the individual arch and arch bridges, it is estimated not just geometrical factor of arch, residual stress, work conditions, geometric imperfections but geometrical nonlinearity too. Geometric nonlinearity especially dominates in many times static indeterminable systems such as network arch bridges. However there are a few represents of estimation of geometric nonlinearity of the new construction form of the arch bridges created in a middle of 20th century. This paper represents estimation of geometric nonlinearity with numerical method of the steel arch bridges with vertical hangers and network arch bridges. There are determined stress-strain law and principal behavior of the steel network arch bridges under symmetric and asymmetric pedestrian loadings. Arkiniai tiltai – vieni populiariausių, seniausių ir grakščiausių tiltų, statomų miesto ir užmiesčio zonose. Tačiau dėl dominuojančios ašinės gniuždymo jėgos arkos tampa ypač jautrios stabilumo praradimui. Siekiant užtikrinti pavienių arkų ir arkinių tiltų pastovumo sąlygas, vertinami ne tik arkos geometriniai rodikliai, darbo stadijos, pradiniai įtempiai, geometriniai netobulumai, bet ir netiesinė konstrukcijos elgsena. Geometrinis netiesiškumas ypač dominuoja daug kartų statiškai neišsprendžiamose sistemose, tokiose kaip tinkliniai arkiniai tiltai. Tačiau šios XX a. viduryje atsiradusios naujos arkinių tiltų konstrukcinės formos geometrinio netiesiškumo vertinimas pateiktas minimaliai. Straipsnyje pateikiamas plieninių arkinių tiltų su vertikaliomis pakabomis ir tinklinių arkinių tiltų geometrinio netiesiškumo vertinimas skaitiniais metodais. Nustatomas plieninių tinklinių arkinių tiltų įtempių-deformacijų būvis ir esminiai elgsenos ypatumai, veikiant simetrine ir asimetrine pėsčiųjų apkrovomis.

scholarly journals A hybrid computational approach for option pricing

2018 ◽  
Vol 05 (03) ◽  
pp. 1850021 ◽  
Author(s):  
Song-Ping Zhu ◽  
Xin-Jiang He
Keyword(s):  
Option Pricing ◽  
Hybrid Approach ◽  
Life Time ◽  
Small Region ◽  
Numerical Approach ◽  
Computational Approach ◽  
Option Prices ◽  
Current Value ◽  
Mc Simulation ◽  
Special Case

In this paper, we propose a novel numerical approach for option pricing with the combination of the MC (Monte Carlo) simulation and the PDE (partial differential equation) approach. Our motivation originates from the fact that within a finite life time of an option contract, the underlying price as well as the range of volatility are expected to vary within a relatively small region centered around the current value of the underlying and the volatility and hence there is no need to compute option prices for the underlying and the volatility values beyond this region. Thus, our hybrid approach takes the advantage of both the MC simulation and PDE approach to form an approach that takes the MC simulation as a special case with the region being extremely small and the PDE approach as another special case with the region being extremely large. Through numerical experiments, we demonstrate that such a hybrid approach enhances computational efficiency, while maintaining the same level of accuracy when either the MC simulation or the PDE approach is used alone for the option prices computed within a suitably chosen interested region.

scholarly journals GEOMETRICALLY NONLINEAR ANALYSIS OF MICROSWITCHES USING THE LOCAL MESHFREE METHOD

2008 ◽  
Vol 05 (04) ◽  
pp. 513-532 ◽  
Author(s):  
Y. T. GU
Keyword(s):  
Nonlinear Analysis ◽  
Large Deformation ◽  
Geometrical Nonlinearity ◽  
Meshfree Method ◽  
Weak Form ◽  
Deformation Analysis ◽  
Geometrically Nonlinear ◽  
Mems Devices ◽  
Mesh Distortion ◽  
Geometrically Nonlinear Analysis

In the modeling and simulation of microelectromechanical system (MEMS) devices, such as the microswitch, the large deformation or the geometrical nonlinearity should be considered. Due to the issue of mesh distortion, the finite element method (FEM) is not effective for this large deformation analysis. In this paper, a local meshfree formulation is developed for geometrically nonlinear analysis of MEMS devices. The moving least squares approximation (MLSA) is employed to construct the meshfree shape functions based on the arbitrarily distributed field nodes and the spline weight function. The discrete system of equations for two-dimensional MEMS analysis is obtained using the weighted local weak form, and based on the total Lagrangian (TL) approach, which refers all variables to the initial configuration. The Newton–Raphson iteration technique is used to get the final results. Several typical microswitches are simulated by the developed nonlinear local meshfree method. Some important parameters of these microswitches, e.g. the pull-in voltage, are studied. Compared with the experimental results and results obtained by linear analysis, nonlinear meshfree analysis of microswitches is accurate and efficient. It has demonstrated that the present nonlinear local meshfree formulation is very effective for geometrically nonlinear analysis of MEMS devices, because it totally avoids the issue of mesh distortion in the FEM.

Geometrically Nonlinear Vibration Analysis of Thin-Walled Composite Beams

2013 ◽  
Author(s):  
Seher Durmaz ◽  
Metin O. Kaya
Keyword(s):  
Linear Model ◽  
Cross Sections ◽  
Transverse Shear ◽  
Composite Beams ◽  
Beam Model ◽  
Geometrically Nonlinear ◽  
Sweep Angle ◽  
Wide Range ◽  
Thin Walled ◽  
Displacement Based

In this study, accounting for large displacements a geometrically nonlinear theory, which is valid for laminated thin-walled composite beams of open and closed cross sections, is developed. The beam model incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. Moreover, the directionality property of thin-walled composite beams produces a wide range of elastic couplings. In this respect, symmetric lay-up configuration i.e. Circumferentially Asymmetric Stiffness (CAS) is adapted to this model to generate coupled motion of flapwise bending-torsion-flapwise transverse shear. Initially, free vibration analyses are carried out for the linear model of the shearable and the non-shearable thin-walled composite beams. Similar to the linear model, the displacement-based nonlinear equations are derived by the variational formulation, considering the geometric non-linearity in the von Karman sense. Finally, the static and the dynamic analyses for the nonlinear beam model are carried out addressing the effects of transverse shear, fiber-orientation and sweep angle on the nonlinear frequencies and the static response of the beam.

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