A geometrically nonlinear model for predicting the intrinsic film stress by the bending-plate method

1990 ◽  
Vol 26 (5-6) ◽  
pp. 511-525 ◽  
Author(s):  
Brian D. Harper ◽  
Wu Chih-Ping
Keyword(s):  
Nonlinear Model ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Plate Method

On compliance with the requirements of Federal Law No. 384-FL «Technical Regulations on the safety of buildings and structures» in the design of foundations and foundations of bridges

Innotrans ◽  
2021 ◽  
pp. 31-37
Author(s):  
Alexey N. Alekhin ◽  
◽  
Andrey A. Alekhin ◽  
Keyword(s):  
Cost Effectiveness ◽  
Nonlinear Model ◽  
Master's Degree ◽  
Geometrically Nonlinear ◽  
Practical Application ◽  
Federal Law ◽  
Effective Training ◽  
Master’S Degree ◽  
Design Solutions ◽  
Technical Regulations

The article discusses the issue of complying with the requirements of Article 16 of Federal Law No. 384-FL «Technical Regulations on the safety of buildings and structures» on the use of a physically and geometrically nonlinear model adequate to the soil when developing the bases and foundations of bridge supports and other transport structures, which will significantly increase the reliability and cost-effectiveness of design solutions. At the same time, it is necessary to adjust the methodological and instrument support of transport universities for the effective training of bachelor’s and master’s degree students in the methodology of practical application of the geotechnical requirements of Law No. 384-FL.

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.

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

1994 ◽  
Vol 61 (4) ◽  
pp. 872-878 ◽  
Author(s):  
C. B. Masters ◽  
N. J. Salamon
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Ritz Method ◽  
Spherical Shape ◽  
Free Edge ◽  
Boundary Region ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress ◽  
Film Substrate

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Practical Application of a Geometrically Nonlinear Stress-Curvature Relation

1991 ◽  
Vol 239 ◽  
Author(s):  
Christine B. Masters ◽  
N. J. Salamon
Keyword(s):  
Strain Energy ◽  
Film Stress ◽  
Silicon Substrates ◽  
Substrate Thickness ◽  
Geometrically Nonlinear ◽  
Practical Application ◽  
Total Strain Energy ◽  
Initial Film ◽  
Nonlinear Stress ◽  
Film Substrate

ABSTRACTA recently developed geometrically nonlinear stress-curvature relation based on a minimization of the total strain energy, which predicts a bifurcation in shape as the magnitude of intrinsic film stress increases, is discussed in this paper. It is compared with the linear theories of Stoney and Brenner & Senderoff for a thin molybdenum film on silicon substrates with various thicknesses. Although the ratio of film to substrate elastic modulus is only 2, Stoney's equation generates significant error for this film/substrate system and the Brenner & Senderoff relation should be used for calculating initial film stress when plate deflections are small. When deflections exceed approximately half the substrate thickness the Brenner & Senderoff equation produces over 10% error and consequently, the nonlinear stress-deflection relation should be used to relate plate curvatures to initial film stress.

scholarly journals Stability of pinned-rotationally restrained arches

2020 ◽  
pp. 10-10
Author(s):  
László Kiss
Keyword(s):  
Nonlinear Model ◽  
Bending Moment ◽  
Geometrically Nonlinear ◽  
Vertical Force ◽  
Material Distribution ◽  
Nonlinear Load ◽  
Buckling Loads ◽  
Strain Relationship ◽  
Membrane Strain ◽  
End Restraint

The article aims to find the buckling loads for pinned-rotationally restrained shallow circular arches in terms of the rotational end stiffness, geometry and material distribution. The loading is a concentrated vertical force placed at the crown. A geometrically nonlinear model is presented which relates not only the axial force but also the bending moment to the membrane strain. The nonlinear load-strain relationship is established between the strain and load parameters. This equation is then solved and evaluated analytically. It turns out that the stiffness of the end-restraint has, in general, a significant effect on the lowest buckling load. At the same time, some geometries are not affected by this. As the stiffness becomes zero, the arch is pinned-pinned and as the stiffness tends to infinity, the arch behaves as if it were pinned-fixed and has the best load-bearing abilities.

Effect of Initial Substrate Curvature on Nonlinear Bending Measurements of Thin-Film Stress.

1991 ◽  
Vol 239 ◽  
Author(s):  
D. E. Fahnline
Keyword(s):  
Thin Film ◽  
Nonlinear Model ◽  
Nonlinear Effects ◽  
Film Stress ◽  
Principle Of Superposition ◽  
Nonlinear Bending ◽  
Initial Curvature ◽  
Thin Film Stress ◽  
Initial Substrate ◽  
Substrate Curvature

ABSTRACTA recently reported nonlinear model of the bending of a thin-film/substrate bilayer provides a means for determining stress in thin films even for large deflection and ellipsoidal bending. This model replaces the usual Stoney's equation, which is valid only for small deflections. However, the model omits consideration of the commonly observed initial curvature of the substrate before deposition. In the small deflection regime the principle of superposition justifies simply subtracting the initial curvature from the final curvature after deposition, but for large deflections this is inappropriate, because the principle of superposition is no longer valid. The present paper presents a modified form of the nonlinear model incorporating initial substrate bending. The resulting equations show that initial substrate curvature causes magnified nonlinear effects and provide a means for determining film and substrate elastic properties in addition to thin-film stress.

Nonlinear Model and Numerical Solutions of Large Deformation of Functionally Graded Conical Shell

2014 ◽  
Vol 941-944 ◽  
pp. 1548-1551
Author(s):  
Jing Hua Zhang ◽  
Shuai Chen
Keyword(s):  
Large Deformation ◽  
Nonlinear Model ◽  
Conical Shell ◽  
Numerical Solutions ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Functionally Graded Shell

Geometrically nonlinear model and numerical solutions of large deformation of imperfect functionally graded materials conical shell subjected to both mechanical load and transversely non-uniform temperature rise are given. The material properties of functionally graded shell are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. On the basis of geometrically nonlinear theory of shell, governing equations of the axi-symmetrical deformation are derived. Numerical solutions are obtained by using a shooting method.

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