Частичное закрытие прямолинейных трещин со связями в стрингерной пластине с отверстием

Исследуется бесконечная упругая изотропная пластина, имеющая круговое отверстие, из контура которого исходят две симметричные прямолинейные трещины. Полагается, что в зонах трещин, примыкающих к вершинам, между берегами имеют место связи (силы сцепления). Размер концевых зон трещин, где имеются связи, сравним с размером трещин. К пластине симметрично относительно ее поверхности приклепаны поперечные стрингеры. Рассмотрен случай частичного закрытия трещин в концевых зонах. Размер зон контакта берегов трещин заранее неизвестен. Действие стрингеров заменяется неизвестными эквивалентными сосредоточенными силами, приложенными в точках соединения ребер с пластиной. Для определения параметров, характеризующих закрытие трещин, получено сингулярное интегральное уравнение, которое с помощью процедуры алгебраизации сведено к конечной нелинейной алгебраической системе. Решая алгебраическую систему методом последовательных приближений, были найдены силы сцепления в связях, контактные напряжения и размер контактных зон трещин.Досліджується підкріплена стрингерами пружна ізотропна пластина, що має круговий отвір, з якого виходять прямолінійні тріщини зі зв'язками між берегами. Розглянуто випадок часткового закриття тріщин. Для визначення параметрів, що характеризують закриття тріщин, отримано сингулярне інтегральне рівняння, яке за допомогою процедури алгебраізації зведене до скінченної нелінійної алгебраїчної системи. Розв’язуючи алгебраїчну систему методом послідовних наближень, знайдені сили зчеплення в зв’язках, контактні напруження й розмір контактних зон тріщин.An elastic isotropic plate reinforced by stringers and having a circular hole has been considered. From the circular hole two symmetric rectilinear bridged cracks are originate. Size of the cracks end zones (zones with the interfacial bonds) is comparable with size of the cracks. The case of partial closure of the cracks is considered. Size of the zones of the crack faces contact is unknown in advance. Effect of the stringers is replaced by unknown equivalent concentrated forces applied at the points of the ribs and plate joining. For definition of the parameters characterizing the closure of cracks, a singular integral equation has been obtained. The singular integral equation has been reduced to a finite nonlinear algebraic system using the algebraization procedure. Solving the algebraic system by the method of successive approximations, the cohesive forces in the bonds, the contact stresses and the size of the contact zones of the cracks have been found

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells

PhDThis thesis presents new boundary element formulations for solution of bending problems in plates and shells. Also presented are the dual boundary element formulations for analysis of crack problems in plates and shells. Reissner plate theory is adopted to represent the bending and shear, and two dimensional (2-D) plane stress is used to model the membrane behaviour of the plate. New set of boundary element formulations to solve bending problems of shear deformable shallow shells having quadratic mid-surface is derived based on the modified Reissner plate and two dimensional plane stress governing equations which are now coupled due to the curvature of the shell. Dual Boundary Element Methods (DBEM) for plates and shells are developed for fracture mechanics analysis of structures loaded in combine bending and tension. Five stress intensity factors, that is, two for membrane and three for bending and shear are computed. The JIntegral technique and Crack Surface Displacements Extrapolation (CSDE) technique are used to compute the stress intensity factors. Special shape functions for crack tip elements are implemented to represent mom accurately displacement fields close to the crack tip. Crack growth processes are simulated with an incremental crack extension analysis. During the simulation, crack growth direction is determined using the maximum principal stress criterion. The crack extension is modelled by adding new boundary elements to the previous crack boundaries. As a consequence remeshing of existing boundaries is not required, and using this method the simulation can be effectively performed. Finally, a multi-region boundary element formulation is presented for modelling assembled plate-structures. The formulation enforces the compatibility of translations and rotations as well as equilibrium of membrane, bending and shear tractions. Examples are presented for plate and shell structures with different geometry, loading and boundar-y conditions to demonstrate the accuracy of the proposed formulations. The results obtained are shown to be in good agreement with analytical and other numerical results. Also presented are crack growth simulations of flat and curved panels loaded in combine bending and tension. The DBEM results are in good agreement with existing numerical and experimental results. Assembled plate-structure and a non-shallow shell bending problems are also analysed using a multi-region formulation developed in this thesis.PT Industri Pesawat Terbang Nusantara, Bandung, Indonesi

FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance

International technical experts in durability and damage tolerance of metallic airframe structures were assembled to present and discuss recent research findings and the development of advanced design and analysis methods, structural concepts, and advanced materials. The symposium focused on the dissemination of new knowledge and the peer-review of progress on the development of advanced methodologies. Papers were presented on: structural concepts for enhanced durability, damage tolerance, and maintainability; new metallic alloys and processing technology; fatigue crack initiation and small crack effects; fatigue crack growth models; fracture mechanics failure, criteria for ductile materials; structural mechanics methodology for residual strength and life prediction; development of flight load spectra for design and testing; and advanced approaches to resist corrosion and environmentally assisted fatigue

Tube Waves, Seismic Waves And Effective Sources

A simple asymptotic analysis, based on the smallness of the ratio of the borehole radius to the wavelength, reveals the interaction between tube waves and seismic waves. The pressure field in a tube wave acts as a secondary source of seismic waves and conversely an incoming seismic wave excites a tube wave. The asymptotic analysis leads to a characterization of these sources in terms of the solution to two-dimensional elastostatic problems. These may be solved exactly when the borehole has an elliptical cross-section even in an anisotropic formation. Also the borehole need not be straight provided that its radius of curvature is large compared with a wavelength

Enrichment of the Boundary Element Method through the Partition of Unity Method for Fracture Analysis using Local and Global Formulations

The present thesis proposes an innovative technique of applying enrichment to the Boundary Element Method to allow accurate analysis of 2D crack problems. An overview of fracture mechanics is given, with particular emphasis given to numerical methods and the techniques used to extract the highly important stress intensity factors - a measure of the singularity of a crack tip. The Boundary Element Method framework is described and later, the implementation of the new technique of enrichment is defined in detail. Finally, several crack problems are used to verify the accuracy of the method where the results are shown to compare very favourably with other well-established numerical methods

Analysis of plane problems with defects of different geometric shapes

This thesis presents research on a plate with defects of various geometric shapes, including a circular hole, a 'finite-height crack,' a notch, and a parabolic notch. The primary focus of the entire work is to produce analytical solutions for the stress state of a plate containing one of these defects, subjected to different loading modes. Additionally, the thesis explores the unique situation where the plane problem extends into the third dimension, forming a 3D body, and examines the end effects. While the stress state within a plate with a circular hole is a classical problem with a fully solved solution, this thesis delves into the shakedown phenomenon under cyclic loading, offering insights of practical importance. Defects containing one or more singular features are also worth investigating. Singular features are defined as areas where stress is concentrated and tends to infinity in elastic analysis, such as cracks or sharp notches. The general approach to these problems typically involves using asymptotic or approximate solutions, like Williams’ solution. However, this thesis aims to produce a non-approximated, closed-form solution for the stress field of a wedge (with angles ranging from zero to 2π) interacting with a singularity (singular force or dislocation) under the anti-plane loading. This methodology can be extended to a parabolic notch, which is also discussed. The 'finite-height crack' is another example involving singular features, but it has two singularities at a 'short' distance apart. Therefore, the thesis discusses the interaction of the stress state around the two singularities and predicts the location of fracture initiation in a 'finite-height' crack case. Finally, the thesis explores a scenario where a plane problem extends into the third dimension, becoming a 3D problem. An example is presented using plane contact as a reference, employing numerical methods to analyse the 3D end effect. This work provides a clear explanation of how the end effect generalizes at the free end and the distance it propagates in terms of the geometric feature length

A review of fracture mechanics life technology

Lifetime prediction technology for structural components subjected to cyclic loads is examined. The central objectives of the project are: (1) to report the current state of the art, and (2) recommend future development of fracture mechanics-based analytical tools for modeling subcritical fatigue crack growth in structures. Of special interest is the ability to apply these tools to practical engineering problems and the developmental steps necessary to bring vital technologies to this stage. The authors conducted a survey of published literature and numerous discussions with experts in the field of fracture mechanics life technology. One of the key points made is that fracture mechanics analyses of crack growth often involve consideration of fatigue and fracture under extreme conditions. Therefore, inaccuracies in predicting component lifetime will be dominated by inaccuracies in environment and fatigue crack growth relations, stress intensity factor solutions, and methods used to model given loads and stresses. Suggestions made for reducing these inaccuracies include development of improved models of subcritical crack growth, research efforts aimed at better characterizing residual and assembly stresses that can be introduced during fabrication, and more widespread and uniform use of the best existing methods

A high-performance boundary element method and its applications in engineering

As a semi-numerical and semi-analytical method, owing to the inherent advantage, of boundary-only discretisation, the boundary element method (BEM) has been widely applied to problems with complicated geometries, stress concentration problems, infinite domain problems, and many others. However, domain integrals and non-symmetrical and dense matrix systems are two obstacles for BEM which have hindered the its further development and application. This thesis is aimed at proposing a high-performance BEM to tackle the above two drawbacks and broaden the application scope of BEM. In this thesis, a detailed introduction to the traditional BEM is given and several popular algorithms are introduced or proposed to enhance the performance of BEM. Numerical examples in heat conduction analysis, thermoelastic analysis and thermoelastic fracture problems are performed to assess the efficiency and correction of the algorithms. In addition, necessary theoretical derivations are embraced for establishing novel boundary integral equations (BIEs) for specific engineering problems. The following three parts are the main content of this thesis. (1) The first part (Part II consisting of two chapters) is aimed at heat conduction analysis by BEM. The coefficient matrix of equations formed by BEM in solving problems is fully-populated which occupy large computer memory. To deal with that, the fast multipole method (FMM) is introduced to energize the line integration boundary element method (LIBEM) to performs better in efficiency. In addition, to compute domain integrals with known or unknown integrand functions which are caused by heat sources or heterogeneity, a novel BEM, the adaptive orthogonal interpolation moving least squares (AOIMLS) method enhanced LIBEM, which also inherits the advantage of boundary-only discretisation, is proposed. Unlike LIBEM, which is an accurate and stable method for computing domain integrals, but only works when the mathematical expression of integral function in domain integrals is known, the AOIMLS enhanced LIBEM can compute domain integrals with known or unknown integral functions, which ensures all the nonlinear and nonhomogeneous problems can be solved without domain discretisation. In addition, the AOIMLS can adaptively avoid singular or ill-conditioned moment matrices, thus ensuring the stability of the calculation results. (2) In the second part (Part III consisting of four chapters), the thermoelastic problems and fracture problems are the main objectives. Due to considering thermal loads, domain integrals appear in the BIEs of the thermoelastic problems, and the expression of integrand functions is known or not depending on the temperature distribution given or not, the AOIMLS enhanced LIBEM is introduced to conduct thermoelasticity analysis thereby. Besides, a series of novel unified boundary integral equations based on BEM and DDM are derived for solving fracture problems and thermoelastic fracture problems in finite and infinite domains. Two sets of unified BIEs are derived for fracture problems in finite and infinite domains based on the direct BEM and DDM respectively, which can provide accurate and stable results. Another two sets of BIEs are addressed by employing indirect BEM and DDM, which cannot ensure a stable result, thereby a modified indirect BEM is proposed which performs much more stable. Moreover, a set of novel BIEs based on the direct BEM and DDM for cracked domains under thermal stress is proposed. (3) In the third part (Part IV consisting of one chapter), a high-efficiency combined BEM and discrete element method (DEM) is proposed to compute the inner stress distribution and particle breakage of particle assemblies based on the solution mapping scheme. For the stress field computation of particles with similar geometry, a template particle is used as the representative particle, so that only the related coefficient matrices of one template particle in the local coordinate system are needed to be calculated, while the coefficient matrices of the other particles, can be obtained by mapping between the local and global coordinate systems. Thus, the combined BEM and DEM is much more effective when modelling a large-scale particle system with a small number of distinct possible particle shapes. Furthermore, with the help of the Hoek-Brown criterion, the possible cracks or breakage paths of a particle can be obtained

Faktori intenziteta napona višestrukih prslina na duraluminijumskim panelima

The aim of this thesis was to establish and demonstrate significant capacity and performances of extended finite element method (XFEM) to calculate stress intensity factors (SIFs) histories versus crack length for problems involving multiple, interacting cracks resulting from multiple site damage (MSD). The thesis includes two deferent types of a typical aero structural configuration were analyzed: the first was unstiffened flat panel made of aluminum Al 2024-T3, containing 11 holes, each of which is a site for crack growth. Analyzed model makes a unique 3D configuration with 22 cracks, propagating at the same time; the applied stresses were equal to 50,100 and 200 MPa. The computations were carried out in Morfeo/Crack for Abaqus software which relies on the implementation of XFEM. The accuracy of these computations was verified through FRANC2D/L software and superposition based approximate method. The conducted analysis showed that XFEM is efficient tool for the simulation of crack propagation even in the case of 3D configurations with MSD, and that the obtained solutions can be used for the prediction of SIFs in analyzed MSD configuration with acceptable accuracy. The second type of aero structural configuration which analyzed in this research using XFEM as following:- - The first model was unstiffened curved panel with 3 rivet holes containing 6 cracks propagating at the same time; the applied average pressure was (0.054 MPa). - The second model was unstiffened curved panel with 5 rivet holes containing 10 cracks propagating at the same time; the applied pressure was (0.054 MPa). - The third model was unstiffened curved panel with 7 rivet holes containing 14 cracks propagating at the same time; the applied average pressure was (0.054 MPa). - The forth model was unstiffened curved panel with 11 rivet holes containing 22 cracks propagating at the same time; the applied average pressure was (0.054 MPa). STRESS INTENSITY FACTORS EVALUTION AT TIPS OF MULTIPLE SITE CRACKS IN 2024-T3 ALUMINUM PANELS v - All curved panels simulations study includes the relationship between crack length and its corresponding SIFs values for every crack propagation step, Also, the study includes the effect of change fuselage diameters from 1.6m, 2.4 m, 3.2 m to 4 m on every crack of the whole models and its SIF values. - Also, the computations were carried out in Morfeo/Crack for Abaqus software which relies on the implementation of XFEM. The conducted analysis showed that XFEM is efficient tool for the simulation of crack propagation even in the case of 3D configurations with MSD, and that the obtained solutions can be used for the prediction of SIFs in analyzed MSD configuration with acceptable accuracy. - Additionally, the research includes study and comparisons of SIF values for two flat and curved panels which had the same dimensions and number of the cracks (22 cracks); and study the effect of truss by adding frames on the curved model with 22 cracks, the results showed a high decreasing in SIF values. - Finally, the research includes some SIFs calculations using standard model. The calculations are done using the empirical equations and NASGROW software. The comparisons showed excellent and accurate results using both methods.Osnovni cilj ove teze jeste demonstracija mogućnosti i značaja proširene metode konačnih elemenata (PMKE) u izračunavanju vrednosti faktora intenziteta napona (FIN) u slučajevima višestrukih međusobno uticajnih prslina nastalih kao posledica pojave višestrukih oštećenja na strukturi (VOS). Teza obuhvata analizu dve tipične aero-strukturne konfiguracije. Prva od njih je neojačana ravna ploča od duraluminijuma 2024-T3 sa 11 otvora za zakivke, od kojih svaki predstavlja mesto gde je rast prsline vrlo verovatan. Analizirani model čini jedinstvena 3D konfiguracija sa 22 prsline koje rastu istovremeno. Primenjeni naponi na krajevima ploče iznosili su 50, 100 i 200 MPa. Proračuni su sprovedeni u programu Morfeo/Crack for Abaqus koji se oslanja na implementaciju PMKE-a. Tačnost dobijenih rezultata verifikovana je pomoću softvera FRANC2D/L i približne metode zasnovane na principu superpozicije. Izvedena analiza pokazala je da je PMKE efikasan alat za simulaciju širenja prslina u slučaju ravnih 3D konfiguracija sa VOS i da se dobijena rešenja mogu koristiti za predviđanje FIN-a u analiziranoj VOS konfiguraciji sa prihvatljivom tačnošću. Druga aero-strukturna konfiguracija koja je analizirana korišćenjem PMKE u okviru ovog istraživanja sastojala se iz nekoliko modela VOS-a: - Prvi model bio je neojačani zakrivljeni panel sa 3 otvora za zakivke i ukupno 6 prslina koje se istovremeno šire iz otvora; primenjeni diferencijalni pritisak iznosio je 0,054 MPa. - Drugi model bio je neojačani zakrivljeni panel sa 5 otvora za zakivke i ukupno 10 prslina koje se istovremeno šire iz otvora; primenjeni diferencijalni pritisak iznosio je 0,054 Mpa. - Treći model bio je neojačani zakrivljeni panel sa 7 otvora za zakivke i ukupno 14 prslina koje se istovremeno šire iz otvora; primenjeni diferencijalni pritisak iznosio je 0,054 MPa. STRESS INTENSITY FACTORS EVALUTION AT TIPS OF MULTIPLE SITE CRACKS IN 2024-T3 ALUMINUM PANELS vii - Četvrti model bio je neojačani zakrivljeni panel sa 11 otvora za zakivke i ukupno 22 prsline koje se istovremeno šire iz otvora; primenjeni diferencijalni pritisak iznosio je 0,054 Mpa. Sve simulacija širenja višestrukih prslina na zakrivljenim pločama uključuju vezu između dužine prslina i odgovarajućih vrednosti FIN-a za svaki korak širenja prsline. Takođe, u istraživanju je u obzir uzet i efekat promene prečnika krivine panela, pa su vrednosti FIN-a računate za sva četiri modela u slučajevima zakrivljenosti od 1,6 m, 2,4 m, 3,2 m i 4 m. I u ovim slučajevima proračuni su vršeni u programu Morfeo/Crack for Abaqus zasnovan na PMKE. Analiza dobijenih rezultata pokazala je da je PMKE efikasan alat za simulaciju širenja prslina u slučaju 3D konfiguracija sa VOS i da se dobijena rešenja mogu koristiti za predviđanje zamornog veka sa prihvatljivom tačnošću. Pored toga, istraživanje predstavljeno u ovoj tezi uključilo je i proučavanje i upoređivanje vrednosti FIN-a u slučaju ravnog i zakrivljenog panela istih dimenzija i broja prslina (dvadeset i dve), kao i proučavanje efekta ojačanja panela dodavanjem okvira na zakrivljenom modelu sa 22 prsline. Rezultati su pokazali značajno smanjenje vrednosti FIN-a na ojačanom panelu. Najzad, istraživanje je obuhvatilo i određivanje FIN-a korišćenjem standardnih modela u svrhu evaluacije rezultata dobijenih pomoću PMKE. Proračuni su vršeni korišćenjem empirijskih jednačina i NASGRO softvera. Poređenje rezultata je pokazalo vrlo dobro poklapanje vrednosti dobijenih korišćenjem različitih metoda