Dynamic Analysis of an Annular Plate Resting on the Surface of an Elastic Half-Space with Distributive Properties

This work gives a semi-analytical approach for the dynamic analysis of a plate of annular shape resting on the surface of an elastic half-space with distributive properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, the dynamic analysis of beams and plates interacting with the surfaces of elastic foundations has to date not been completely solved. To advance this work, the deflections of the plate are determined by the Ritz method, and the displacements of the surface of elastic half-space are determined by studying Green's function. The coupling of these two studies is achieved by a mixed method, which allows determination of reactive forces in the contact zone and, hence, the determination of other physical magnitudes. Natural frequencies, natural shapes, and the dynamic response of a plate due to external harmonic excitation are determined. Validation with a Winkler problem illustrates the distributive property effects on the results of the dynamic analysis

Geometrically nonlinear analysis for an elastic body by the boundary element method

The subject of this study is that of coupling the boundary element method (BEM) and a finite element-like interpolation procedure for the analysis of elastic bodies undergoing large deformations. The nonlinear integral relationships for the problem are described and presented in detail according to a total Lagrangian approach. The domain is discretized by quadratic boundary elements and interior cells and the displacements of all interior nodes are calculated from the integral representation. The domain variables, which include the deformation gradients and the 2nd Piola-Kirchhoff stresses, are interpolated through a finite element process. The direct technique whereby the deformation gradients are determined from analytical differentiation of the displacement representation, which requires the integration of higher order singularities, is totally eliminated. This allows for an easier calculation of the domain terms which account for the nonlinear portion of the problem. An iteration procedure is used to solve the integral formulation and numerical calculations are performed for several example problems. In each example, comparison is made with finite element method (FEM) solutions and, whenever possible, with the analytic solutions. These comparisons demonstrate the applicability, effectiveness and limitations of the proposed approach

Interakce vnitřních sil působících na železobetonové průřezy

The dissertation begins by providing a concise overview of linear analysis for beams while accounting for the nonuniformity due to torsion and flexure. The objective is to develop a numerical method based on the finite element method (FEM) to address the Saint-Venant problem with arbitrary cross-sections, building upon Gruttmann's numerical method. In the first part, the author's proposed numerical model considers the shear lag effect caused by torsion and flexure using FEM. Furthermore, it investigates the phenomenon of bending-induced shear lag in arbitrary cross-sections of homogeneous materials. The non-uniform torsion problem and the shear deformation effect in thin-walled beams with arbitrary cross-sections made of homogeneous isotropic elastic material are also examined. Finally, the first part of the dissertation proposes an advanced beam theory that enhances the work of Sapountzakis and Dikaros through minor modifications. The second part of this dissertation is devoted to investigating the nonlinear analysis of reinforced concrete structures. The primary focus of this study is to examine the primary shear warping function profile of reinforced concrete sections under the effect of shear warping, which is still an unexplored topic in structural engineering. To simplify the computational process, the study uses the uniaxial stress-strain relationship and neglects the tensile strength of the concrete for nonlinear analysis. In the nonlinear analysis of beams, the displacement-based approach usually requires a two-step iteration process at both the section and element levels. To simplify this process, the author presents an alternative approach where the ultimate load is determined by detecting whether the concrete strain in the cross-section reaches or exceeds its ultimate strain and whether the Euclidean norm of the unbalanced force exceeds 1. This approach simplifies the previously complex iterative method used for force equilibrium at the element level. The proposed method employs the Newton-Raphson method to capture the plastic mechanism. The author validates the proposed approach through local and global analysis in this study. The dissertation presents significant findings regarding the validity of clauses 6.2.3 (7) and 9.2.1.3 (2) of EN 1992-1-1 (2004) concerning the interaction of shear and flexure. The numerical approach proposed in this research aligns with other reinforced concrete section analysis models and appropriately accounts for moment redistribution in the structural response. The outcomes of the global analysis demonstrate that the proposed method meets the safety and economic criteria. Moreover, the study highlights the underestimation of shear strength in EN 1992-1-1 (2004) compared to ACI 318-19, CSA A23:3:19, and Fib MC 2010 with Level of Approximation (LoA) III. Furthermore, numerical analysis demonstrates that the prescribed limits on moment redistribution outlined in EN 1992-1-1 (2004), ACI 318-19, and CSA A23.3:19 need not be reduced during moment distribution. The study on nonlinear analysis aims to solely present and validate the interaction between shear and flexure in simple cross-sections. However, it should be emphasized that this study simplified the investigation by focusing only on the interaction between shear and flexure. Future research will address the impact of transverse reinforcement and explore the interaction between shear, flexure, and torsion in complex cross-sections.Disertační práce začíná stručným přehledem lineární analýzy nosníků při zohlednění deformací způsobených kroucením a ohybem. Cílem je vyvinout numerickou metodu založenou na metodě konečných prvků (MKP) pro řešení Saint-Venantova problému na průřezech libovolného tvaru, která vychází z Gruttmannovy numerické metody. V první části se v autorem navrženém numerickém modelu pomocí MKP řeší vliv smykového ochabnutí způsobeného kroucením a ohybem. Především pak smykové ochabnutí vyvolané ohybem obecných průřezů z homogenních materiálů. Zkoumá se také problém smykového ochabnutí vyvolaného kroucením a účinek smykové deformace u tenkostěnných nosníků s libovolnými průřezy z homogenního izotropního pružného materiálu. V závěru první části disertační práce je navržena pokročilá teorie nosníků, která drobnými úpravami rozšiřuje práci Sapountzakise a Dikarose. Druhá část disertační práce se věnuje zkoumání železobetonových konstrukcí pomocí nelineární analýzy. Primárně se zaměřuje na zkoumání tvaru funkce deplanace ve smyku u železobetonových průřezů, což je ve stavebním inženýrství dosud neprobádané téma. Pro zjednodušení výpočetního procesu se v práci používá pro nelineární analýzu jednoosý vztah napětí a deformace a zanedbává pevnost betonu v tahu. Při nelineární analýze nosníků vyžaduje deformační přístup obvykle dvoustupňový iterační proces na úrovni průřezu i prvku. Pro zjednodušení tohoto procesu autor předkládá alternativní přístup, kdy se mezní zatížení určuje na základě zjištění, zda deformace betonu v průřezu dosáhne nebo překročí jeho mezní přetvoření a zda euklidovská norma nevyvážené síly překročí hodnotu 1. Tento přístup zjednodušuje dříve používanou složitou iterační metodu pro silovou rovnováhu na úrovni prvku. Navrhovaná metoda využívá k analýze plastického chování Newton-Raphsonovu metodu. Autor v této studii ověřuje navržený přístup pomocí lokální a globální analýzy. V disertační práci jsou uvedena významná zjištění týkající se platnosti ustanovení 6.2.3 (7) a 9.2.1.3 (2) normy EN 1992-1-1 (2004) související s interakcí smyku a ohybu. Numerický přístup navržený v této práci je v souladu s jinými modely analýzy železobetonových průřezů a vhodně zohledňuje přerozdělení vnitřních sil v odezvě konstrukce. Výsledky globální analýzy ukazují, že navržená metoda splňuje bezpečnostní a ekonomická kritéria. Studie navíc upozorňuje na podhodnocení smykové pevnosti v normě EN 1992-1-1 (2004) ve srovnání s normami ACI 318-19, CSA A23:3:19 a Fib MC 2010 s úrovní přiblížení (LoA) III. Numerická analýza dále ukazuje, že předepsané meze přerozdělení momentů uvedené v normách EN 1992-1-1 (2004), ACI 318-19 a CSA A23.3:19 není třeba měnit. Výhradním cílem studie v oblasti nelineární analýzy je prezentovat a ověřit interakci mezi smykem a ohybem na jednoduchých průřezech. Je však třeba zdůraznit, že tato studie zjednodušila vyšetřování právě tím, že se zaměřila pouze na interakci těchto dvou složek vnitřních sil. Budoucí výzkum se bude zabývat vlivem příčné výztuže a zkoumat interakci mezi smykem, ohybem a krutem ve složitých průřezech.221 - Katedra konstrukcívyhově

Applications of Isogeometric Analysis Coupled with Finite Volume Method

In this thesis, a combination of Isogeometric Analysis (IGA) and Finite Volume Method (FVM) on geometries parameterized by Non-Uniform Rational Basis Splines (NURBS) is explored with applications in fluid flow, heat transfer, and shape optimization. An IGA framework supplemented with FVM is created in MATLAB® to solve problems defined over single patch domains with mesh refinement by node insertion. Additionally, a second-order finite difference method is developed using non-orthogonal curvilinear coordinates and a numerical Jacobian of the NURBS geometry. The examples include fully developed laminar flow through ducts, potential flow around a tilted ellipse, transient heat conduction, linear advection-diffusion, and a basic shape optimization example using a particle swarm technique. The numerical results are compared among the methods and verified with available analytical solutions

On 3-D inelastic analysis methods for hot section components (base program)

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report

Dynamic Boundary Element Analysis of Machine Foundations

The central theme of this thesis is the further development of boundary element methods for the analysis of three-dimensional machine foundations, pertaining to various (translational and rotational) modes of vibration and, in particular, to high frequency response. Surface and embedded rectangular foundations are considered. The soil is assumed to behave approximately as a linear elastic material for small amplitudes of strain. The problem is formulated and solved in the frequency domain. This work includes rigorous theoretical studies, effective numerical techniques for the solution of the boundary integral equations, and efficient computer implementation of the algorithm. The derivation of the boundary integral formulation is reviewed and the dynamic fundamental solutions are examined in detail. The particular fundamental solutions for incompressible media has been derived in order to deal more effectively with these materials. Advanced integration schemes for non-singular and singular integrals have been developed in order to improve the computational accuracy and efficiency of the boundary element analysis. A novel infinite boundary element for dynamic analyses has been developed, which provides an efficient means for including far-field effects, without the necessity of explicit discrete representation outside the near field. The implementation and vectorization of the computer program using the IBM 3090-150 Vector Facility is described. Various numerical results for rectangular foundations are presented in order to illustrate the potential of the infinite boundary element formulation. Included among these are new results pertaining to the high frequency response of machine foundations

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established