A weight function technique in three-dimensional fracture mechanics: static and dynamic

1996 ◽  
Vol 78 (2) ◽  
pp. 101-115 ◽  
Author(s):  
P. H. Wen ◽  
M. H. Aliabadi ◽  
D. P. Rooke
Keyword(s):  
Fracture Mechanics ◽  
Weight Function ◽  
Three Dimensional ◽  
Function Technique

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

An Investigation of the Structural Dynamics of a Racing Yacht

1999 ◽  
Author(s):  
Frederic Louarn ◽  
Pandeli Temarel
Keyword(s):  
Dynamic Properties ◽  
Three Dimensional ◽  
Element Model ◽  
Point Of View ◽  
Mode Shapes ◽  
Function Technique ◽  
Operational Conditions ◽  
Principal Coordinates ◽  
Modal Summation ◽  
Structural Responses

The dynamic behaviour of a WOR 60 is investigated using three dimensional hydroelasticity theory. Global structural responses (e.g. stresses) in waves are obtained corresponding to the upright as well as to the more realistic heeled sailing configurations, revealing the connection between the ballast keel and the hull as being a critical area of the structure. For the "dry hull" analysis, a global finite element model has been developed, incorporating the hull and deck shell, the internal structure, the ballast keel and the rig together with rigging loads. The modular nature of the model has been used to assess the relative influence of each of the aforementioned components upon the required characteristic dynamic properties (e.g. natural frequencies and principal mode shapes). Regarding the "wet hull" analysis, a three dimensional Green's function technique, using pulsating sources distributed over the wetted surface, provides a numerical solution to the case of the yacht sailing in regular waves at arbitrary heading. Principal coordinates for the rigid body motions and flexible distortions of interest are evaluated and the latter are used to obtain the dynamic stresses in waves using modal summation. This paper will describe the modelling techniques used and discuss the applicability / limitations of hydroelasticity theory regarding this type of structures in the light of the results obtained for the upright and heeled operational conditions, as well as from the point of view of design aspects such as "L" and "T" keel configurations. The ABS design criteria will provide a practical reference for comparing the results from the dynamic analysis.

scholarly journals The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2320 ◽  
Author(s):  
Ke Li ◽  
Shuangxi Jing ◽  
Jiangong Yu ◽  
Xiaoming Zhang ◽  
Bo Zhang
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Wave Mode ◽  
Functionally Graded ◽  
Function Technique ◽  
Complex Wave ◽  
Acoustic Wave Devices ◽  
Functionally Graded Piezoelectric

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

scholarly journals Fracture mechanics of the three-dimensional crack front: vertex singularity versus out of plain constraint descriptions

2010 ◽  
Vol 2 (1) ◽  
pp. 2095-2102 ◽  
Author(s):  
Pavel Hutař ◽  
Martin Ševčík ◽  
Luboš Náhlík ◽  
Michal Zouhar ◽  
Stanislav Seitl ◽  
...  
Keyword(s):  
Fracture Mechanics ◽  
Crack Front ◽  
Three Dimensional ◽  
Vertex Singularity

Advances in Three-Dimensional Fracture Mechanics

2006 ◽  
Vol 312 ◽  
pp. 27-34 ◽  
Author(s):  
Wan Lin Guo ◽  
Chongmin She ◽  
Jun Hua Zhao ◽  
Bin Zhang
Keyword(s):  
Fracture Mechanics ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Unified Theory ◽  
Constraint Factor ◽  
Engineering Structures ◽  
The Past ◽  
Fatigue And Fracture ◽  
Fracture Theory ◽  
Historical Developments

The historical developments of the fracture mechanics from planar theory to threedimensional (3D) theory are reviewed. The two-dimensional (2D) theories of fracture mechanics have been developed perfectly in the past 80 years, and are suitable for some specific cases of engineering applications. However, in the complicated 3D world, the limitation of the 2D fracture theory has become evident with development of the structure toward complication and micromation. In the 1990’s, Guo has proposed the 3D fracture theory with a 3D constraint factor based on the deformation theory and energy theory. The proposed 3D theory can predict accurately the fracture problems for practical and complicated engineering structures with defects, by integrating the 3D theory of fatigue, which has been developed to unify fatigue and fracture. Our efforts to develop the 3D fracture mechanics and the unified theory of 3D fatigue and fracture are summarized, and perspectives for future efforts are outlined.

Fracture Mechanics Analysis of a PWR Under PTS Using XFEM and Input From TRACE

2019 ◽  
Author(s):  
Diego F. Mora ◽  
Roman Mukin ◽  
Oriol Costa Garrido ◽  
Markus Niffenegger
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Element Model ◽  
Integrity Assessment ◽  
Mechanics Analysis ◽  
Dynamic Cooling

Abstract In this paper, an integrity assessment of a reference Reactor Pressure Vessel (RPV) under Pressurized Thermal Shock (PTS) is performed. The assessment is based on a multi-step simulation scheme, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses. The proposed strategy uses a three dimensional (3D) finite element model (FEM) of the RPV with the Abaqus code to solve the thermo-mechanical problem for the scenario of a Large-Break Loss-of-Coolant Accident (LBLOCA). In order to obtain the boundary conditions for the thermal analysis, the thermo-hydraulic results from a 3D RPV model developed in the system code TRACE are used. The fracture mechanics analysis is carried out on submodels defined on the areas of interest. Submodels containing cracks or flaws are also located in regions of the RPV where there might be a concentration of stresses during the PTS. The calculation of stress intensity factor (SIF) makes use of the eXtended FEM (XFEM) approach. The computed SIF of the postulated cracks at the inner surface of the RPV wall are compared with the ASME fracture toughness curve of the embrittled RPV material. For different transient scenarios, the boundary conditions were previously calculated with a computational fluid dynamics (CFD) model. However, cross-verification of the results has shown consistency of both CFD and TRACE models. Moreover, the use of the later is very convenient for the integrity analyses as it is clearly less computationally expensive than CFD. Therefore, it can be used to calculate different PTS scenarios including different break sizes and break locations. The main findings from fracture mechanics analyses of the RPV subjected to LBLOCA are summarized and compared. The presented results also allow us to study the influence of the dynamic cooling plume on the stress intensity factor in more detail than with the conventional one-dimensional method. However, the plumes calculated with both approaches are different. How much this difference affects the integrity assessment of the RPV is discussed in the paper.

scholarly journals Fixed Point Root-Finding Methods of Fourth-Order of Convergence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 769 ◽  
Author(s):  
Alicia Cordero ◽  
Lucía Guasp ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Nonlinear Problems ◽  
Dynamical Analysis ◽  
Function Technique ◽  
Weight Functions ◽  
Good Tool ◽  
Quadratic Polynomials ◽  
Root Finding ◽  
The Stability

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub’s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.

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