Geometrically Nonlinear Stress Recovery in Composite Laminates Subjected to Dynamic Loading

2014 ◽  
Author(s):  
Timothy Hartman ◽  
Michael W. Hyer ◽  
Scott Case
Keyword(s):  
Dynamic Loading ◽  
Composite Laminates ◽  
Stress Recovery ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress

scholarly journals Geometrically Nonlinear Stress Recovery in Composite Laminates

AIAA Journal ◽  
2012 ◽  
Vol 50 (5) ◽  
pp. 1156-1168 ◽  
Author(s):  
Timothy B. Hartman ◽  
Michael W. Hyer ◽  
Scott W. Case
Keyword(s):  
Composite Laminates ◽  
Stress Recovery ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress

Stress Recovery in Composite Laminates Including Geometrically Nonlinear and Dynamic Effects

AIAA Journal ◽  
2016 ◽  
Vol 54 (8) ◽  
pp. 2521-2529 ◽  
Author(s):  
Timothy B. Hartman ◽  
Michael W. Hyer ◽  
Scott W. Case
Keyword(s):  
Composite Laminates ◽  
Stress Recovery ◽  
Geometrically Nonlinear ◽  
Dynamic Effects

Assessment of Stress-Displacement State of Cable Suspended Pipeline Bridge During Inspection Pig Motion

2016 ◽  
Author(s):  
Igor Orynyak ◽  
Igor Burak ◽  
Sergiy Okhrimchuk ◽  
Andrii Novikov ◽  
Andrii Pashchenko
Keyword(s):  
Stress State ◽  
Dynamic Loading ◽  
System Analysis ◽  
Optical Measurement ◽  
Time Moment ◽  
Dynamic Loads ◽  
Natural Mode ◽  
Geometrically Nonlinear ◽  
Cable System ◽  
Stress Calculation

Designing and maintenance of pipeline cable bridge with dynamic loads is complex because this problem belongs to the geometrically nonlinear problems. Analysis shown that existing mathematics models of cables have restrictions in use and we can’t use these cable models for dynamic loads calculations of cable-suspended pipeline bridge. Movement, produced by motion of inspection pig inside pipeline is an example of such dynamic loads. During its motion through the pipeline cable bridge the inspection pig induces additional stresses in pipeline due its weight and finite velocity which induces the vibration of the bridge. Its stress state assessment requires a lot of modeling, measuring and calculating actions to be done. First of all the initial static stress state of the cable bridge should be evaluated. It depends on the existing tension forces in the cable elements. They approximately were derived from the optical measurement of their geometrical curvatures with accounting for known weight density of the cables. Then, existing software tool for piping stress calculation “3D Pipe Master”, which operates by 12 degrees of freedom in pipe elements, was modernized to be able to take into account the geometrically nonlinear behavior of 6 d.o.f. cable elements. The equations which relate the elongations and rotations of cable elements with tension forces in cables are written in the form convenient for application of the transfer matrix method in the linearized iteration procedure which adjusts the measured displacements of the elements of the bridge with calculated one. In this way the initial tension forces in cables, in particular, and the bridge state, in general were determined. The dynamic part of the problem is solved by expansion in terms of natural frequencies eigenfunctions. Given inspection pig velocity calculation allows to determine the time dependence of generalized loads for each of natural vibration mode as product of the pig weight multiplied by mode shape displacement in point of pig position at the given time moment. Eventually the technique of Duhamel integral is used to calculate the dynamic behavior of the bridge for each natural mode of vibration. Two examples of dynamic stress calculation are considered. First is primitive one and relate to calculation joint interaction pipeline and cable system at dynamic loading. The second example concerns dynamic calculation pipeline cable bridge through the river Svicha during movement inspection pig. This bridge consists of two support, two parallel pipelines (1220×15) with bends and cable system. Analysis shown possibility uses “3D Pipe Master” software for the solving problems of durability pipeline cable bridge any complexity in the conditions of static and dynamic loading.

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.

A New Class of Damage Variables in Continuum Damage Mechanics

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Composite Laminates ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Higher Order ◽  
Cross Sectional Area ◽  
Scalar Case ◽  
Sectional Area ◽  
Cross Sectional ◽  
Nonlinear Stress

In this work various new proposed damage variables are introduced, examined and compared. Only the scalar case pertaining to isotropic damage is investigated here. Several types of new damage variables are proposed as follows: (1) damage variables that are defined in terms of cross-sectional area, (2) damage variables that are defined in terms of the elastic modulus or stiffness, and (3) composite damage variables that are defined in terms of two parameters relating to both cross-sectional area and stiffness. However, the generalization to tensors and general states of deformation and damage may be a straightforward process but is beyond the scope of this work. The damage variables introduced in this work can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. In the second part of this work, higher-order strain energy forms are proposed. It is seen that a specific nonlinear stress-strain relationship is associated with each higher-order strain energy form. These higher order strain energy forms along with some of the proposed damage variables are used in trying to lay the theoretical groundwork for the design of undamageable materials, i.e., materials that cannot be damaged where the value of the damage variable remains zero throughout the deformation process.

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