In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

. The moment-resistant steel frames are frequently used as a load-bearing structure of buildings. Global response of a moment-resistant frame structure strongly depends on connections behavior, which can significantly influence the response and load-bearing capacity of a steel frame structure. The analysis of a steel frame with included joints behavior is the main focus of this work. In particular, we analyze the behavior of two connection types through experimental tests, and we propose numerical beam model capable of representing connection behavior. The six experimental tests, under monotonic and cyclic loading, are performed for two different types of structural connections: end plate connection with an extended plate and end plate connection. The proposed damage-plasticity model of Reissner beam is able to capture both hardening and softening response under monotonic and cyclic loading. This model has 18 constitutive parameters, whose identification requires an elaborate procedure, which we illustrate in this work. We also present appropriate loading program and arrangement of measuring equipment, which is crucial for successful identification of constitutive parameters. Finally, throughout several practical examples, we illustrate that the steel structure connections are very important for correct prediction of the global steel frame structure response.

Cette these traite de l'analyse limite des structures de châssis en acier, qui s'utilise souvent comme la structure principale de support des bâtiments. La structure du cadre en acier est caracterisee par une reponse tres ductile et un grand potentiel pour dissiper l'energie, ce qui est crucial pour la resistance par rapport aux tremblements de terre. La ductilite dans la reponse de la structure est la cause du comportement du materiau lui-meme et du comportement des connexions entre les elements de la structure. Les connexions entre les poutres et les poteaux peuvent influencer de maniere significative la reponse de la structure du cadre en acier, parfois jusqu'a 30%. L'idee est de integrer le comportement des connexions par les elements de poutres qui seront situes dans les coins du cadre et la modelisation du reste serra fait avec des elements de poutres non-lineaires qui decrirons le comportement des poutres en acier. Cette recherche est composee de deux parties. La premiere partie est consacree au comportement des connexions structurelles, la deuxieme partie presente le developpement de l'element fini du faisceau non lineaire capable de representer le comportement ductile d'un element de la structure en acier. Dans la premiere partie de la these, nous definissons la procedure d'identification des parametres constitutifs pour le modele couple de plasticite-degâts avec dix-huit inconnus. Ce modele constitutif est tres robuste et capable de representer une large gamme de problemes. La procedure definie a ete utilisee dans la preparation de tests experimentaux pour trois types de connexions en acier structure. Les tests experimentaux ont ete effectues pour deux cas de charge. Pour la premiere, la charge a ete appliquee dans un sens avec les cycles de chargement et de dechargement. A partir des mesures experimentales, nous avons conclu que le modele de plasticite peut bien representee le comportement de la connexion structurale. Parametres constitutifs ont ete determines a partir des resultats de l'experimentation, on a utilise une poutre geometriquement exacte avec la loi bilineaires renforcement du materiel et la loi lineaire pour le ramollissement. Egalement, on a effectue des essais experimentaux de deux types de raccords en acier en cas de chargement cyclique. Les donnees mesurees montrent que le modele de la plasticite n'est pas assez bon pour decrire le comportement de connexion pour ce type de charge. A savoir, en raison de changements du sens de l'application du chargement, les connexions montrent moins de rigidite, qui peut etre decrite avec un modele constitutif de dommages. Pour cette raison, nous avons developpe un nouveau modele plasticite-dommages qui est capable d'inclure le phenomene mentionne ci-dessus. A la fin de cette section est faite l'identification des parametres constitutifs. La deuxieme partie de la these de doctorat est compose de formulations theoriques et la mise en œuvre numerique des faisceaux geometriquement exacte. La reponse de durcissement de la poutre comprend l'interaction entre les forces de la section resultant du stress (N, T et M), et la reponse de ramollissement est definit par la loi non lineaire. Ce type d'element fini de poutre est capable de decrire le comportement ductile des structures en acier et inclure les effets du second ordre, qui sont tres importantes pour l'analyse ultime des structures de cadre en acier. L'element fini developpe de poutre geometriquement exacte et les lois definies de liaison de comportement dans la construction en acier, offrant la possibilite d'une analyse de haute qualite des structures en acier. En utilisant les modeles de poutre propose et la methodologie de modelisation des structures de châssis en acier, il est possible de determiner une distribution realiste des forces de section transversale , y compris la redistribution due a la formation de rotules plastiques.

In this paper we present methodology for parameters identification of constitutive model which is able to present behavior of a connection between two members in a structure. Such a constitutive model for frame connections can be cast in the most general form of the Timoshenko beam, which can present three failure modes. The first failure mode pertains to the bending in connection, which is defined as coupled plasticity-damage model with nonlinear softening. The second failure mode is seeking to capture the shearing of connection, which is defined as plasticity with linear hardening and nonlinear softening. The third failure mode pertains to the diffuse failure in the members; excluding it leads to linear elastic constitutive law. Theoretical formulation of this Timoshenko beam model and its finite element implementation are presented in the second section. The parameter identification procedure that will allow us to define eighteen unknown parameters is given in Section 3. The proposed methodology splits identification in three phases, with all details presented in Section 4 through three different examples. We also present the real experimental results. The conclusions are stated in the last section of the paper.

The optimal mix of solid waste from the meat industry (MI) for anaerobic digestion (AD) treatment can be selected by defining the biomethane potential (BMP test) of the waste in relation to the unit value of chemical oxygen demand (COD). In this paper, the BMP test of biodegradable wastes from MI has been performed. For the purposes of the experiment, two types of input substrates have been defined: manure (manure from cattle depots and transport vehicles for cattle transport) labeled as O1 and inedible offal, contents of the stomach, sludges from washing and cleaning, and the remains of meat defined as waste O2. According to the BMP test, mixtures of fresh inoculum (38 g), waste O1 and waste O2 in quantities of 1 g and 2 g have been tested, and the model for the selection of the best mix in terms of the biogas yield has been defined. Based on correlations of CH 4 and COD, mixture M1 (O1 : O2 = 80 : 20) is recommended, for treatment at the plant, because it has the highest yield of 256.16 mL CH 4 per unit value of COD.

. In this paper we present geometrically exact Kirchhoff’s initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner’s geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff’s constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite’s polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.