Calculation of a Multi-storey Monolithic Concrete Building on the Earthquake in Nonlinear Dynamic Formulation

AbstractThe article deals with a multi-storey monolithic concrete building calculation on the earthquake. The problem is solved in the time domain by a direct dynamic method. Direct integration of motion equations is carried out on an explicit scheme. This technique allows us to solve the problem in a nonlinear dynamic formulation considering geometric and physical nonlinearities. The paper presents and analyzes the main results of the calculation

VERIFICATION OF ELASTOMERIC BEARINGS FINITE-ELEMENT MODELS IN CALCULATING SOFTWARE PACKAGES

Introduction. While designing buildings and constructions with an elastomeric bearing with a lead core as a seismic isolation system, it is necessary to make calculations concerning effectiveness and reasonability of its usage. These demands lead to necessity to construct bearings in a common finite-element model, in order to consider how a bearing and a construction work together. Though a calculator has a lot of different variants of elastomeric bearing’s construction, which are connected to their implemented work model. To prove that obtained calculation results are sufficient and accurate, selection criteria of elastomeric bearings implemented work models are necessary. Materials and methods. To get accurate results we will compare elastomeric bearing’s work diagrams and free periods of motion when there are different variants of their numerical modelling with the help of software packages with factory tests results. Results. The researches have shown that lateral force’s and shear’s limit values are the same for all of the observed cases, although free periods of motion and work diagrams differ. Usage of more accurate bearing work model in software package Ansys/LS-Dyna can explain these differences, it can be seen if compare their work’s diagrams. Conclusions. Analysis of constructions with elastomeric bearings’ work, which function according to the idealized linear model, can be possible only for II level constructions. Idealized nonlinear models should be used for I level constructions

NEXP-completeness and Universal Hardness Results for Justification Logic

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that the general NEXP upper bound from our previous work is tight. We then use a simple modification of the corresponding reduction to prove that satisfiability for all multi-agent justification logics from there is hard for the Sigma 2 p class of the second level of the polynomial hierarchy - given certain reasonable conditions. Our methods improve on these required conditions for the same lower bound for the single-agent justification logics, proven by Buss and Kuznets in 2009, thus answering one of their open questions.Comment: Shorter version has been accepted for publication by CSR 201

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic

TR-2014003: On the Complexity of Two-Agent Justification Logic

We investigate the complexity of derivability for two-agent Justification Logic. For this purpose we revisit Yavorskaya’s two-agent LP with interactions (2008), we simplify the syntax and provide natural extensions. We consider two-agent versions of other justification logics as well as ways to combine two justification logics. For most of these cases we prove that the upper complexity bound established for the single-agent cases are maintained: these logics ’ derivability problem is in the second step of the polynomial hierarchy. For certain logics, though, we discover a complex-ity jump to PSPACE-completeness, which is a new phenomenon for Justification Logic

Consolidation of Belief in Two Logics of Evidence

Recently, several logics have emerged with the goal of modelling evidence in a more relaxed sense than that of justifications. Here, we explore two of these logics, one based on neighborhood models and the other being a four-valued modal logic. We establish grounds for comparing these logics, finding, for any model, a counterpart in the other logic which represents roughly the same evidential situation. Then we propose operations for consolidation, answering our central question: What should the doxastic state of a rational agent be in a given evidential situation? These operations map evidence models to Kripke models. We then compare the consolidations in the two logics, finding conditions under which they are isomorphic. By taking this dynamic perspective on belief formation we pave the way for, among other things, a study of the complexity, and an AGM-style analysis of rationality of these belief-forming processes