Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading

The displacement-based finite element method dominates current practice for material nonlinear analysis of structures. However, there are several characteristics that may limit the effectiveness of this approach. In particular, for elastoplastic analysis, the displacement method relies upon a step-by-step incremental approach stemming from flow theory and also requires significant mesh refinement to resolve behavior in plastic zones. This leads to computational inefficiencies that, in turn, encourage the reconsideration of force-based approaches for elastoplastic problems.One of these force algorithms that has been recently developed is the large increment method. The main advantage of the flexibility-based large increment method (LIM) over the displacement method is that it separates the global equilibrium and compatibility equations from the local constitutive relations. Consequently, LIM can reach the solution in one large increment or in a few large steps, thus, avoiding the development of cumulative errors. This paper discusses the extension of the large increment methodology for the nonlinear analysis of plane frame structures controlled by an elastic, perfectly plastic material model. The discussion focuses on the power of LIM to handle these nonlinear problems, especially when plastic hinges form in the frame and ultimately as the structure approaches the collapse stage. Illustrative planar frame examples are presented and the results are compared with those obtained from a standard displacement method.     

<Emphasis Type="Italic">p</Emphasis>-Adic mathematical physics and B. Dragovich research

We present a brief review of some parts of p-adic mathematical physics related to the scientific work of Branko Dragovich on the occasion of his 70th birthday.     

Preconditioning of Axillary Buds in Thidiazuron-Supplemented Liquid Media Improves In Vitro Shoot Multiplication in <Emphasis Type="Italic">Nyctanthes arbor-tristis</Emphasis> L.

An efficient tissue culture technology has been designed for mass multiplication of Nyctanthes arbor-tristis L. by preculturing nodal explants in thidiazuron (TDZ)-supplemented liquid Murashige and Skoog (MS) media. Direct inoculation of nodal segments on semi-solid MS medium augmented with various concentrations of TDZ (0.1 to 0.9 μM) produced shoots but with low regeneration response and few shoots per explant. Hence, nodal explants were pretreated with greater concentrations of TDZ (5 to 100 μM) in liquid MS media for different durations (4, 8, 12, and 16 days) with the aim of improving shoot regeneration response from cultured explants. After pretreatment, explants were transferred to agar-solidified hormone-free MS medium. Best response in terms of percent regeneration (94%), number of shoots per explant (20.00 ± 1.15), and greatest shoot length (7.23 ± 0.83 cm) were obtained with nodal segments pretreated in75 μM TDZ for 8 days. Similarly, root induction was obtained from pulse-treated microshoots for 24 h with 200 μM indole-3-butyric acid (IBA) followed by their transfer to 1/2 MS medium which produced an average of 5.50 ± 0.92 roots per microshoot. The rooted plantlets were transplanted to soil with 80% success rate.     

Spatial Wilson loops in a fully anisotropic model

Theoretical and Mathematical Physics - We study spatial Wilson loops for a fully anisotropic background metric supported by the Einstein action with a dilaton field and three Maxwell tensors. We...     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

Demicompactness Results for Strongly Continuous Semigroups,Generators and Resolvents

Let \((U(t))_ {t\ge 0}\) be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) \(t>0\). In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space.     

Stable exact solutions in cosmological models with two scalar fields

We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.