This is the second in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper, a stochastic meshless method is presented for probabilistic fracture-mechanics analysis of linear-elastic cracked structures. The method involves an element-free Galerkin method for calculating fracture response characteristics; statistical models of uncertainties in ...

The current paper presents an effective methodology for assessing the reliability of electromagnetic designs when considering uncertainties of design variables. To achieve this goal, the reliability index approach based on the first-order reliability method is adopted to deal with probabilistic constraint functions, which are expressed in terms of random design variables. The proposed method is...

This paper presents a new method for continuum-based shape sensitivity and reliability analyses of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh pertu...

We prove an institutional version of A. Robinson’s Consistency Theorem. This result is then applied to the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

Henkin, Monk and Tarski gave a compositional semantics for first-order predicate logic. We extend this work by including function symbols in the language and by giving the denotation of the atomic formula as a composition of the denotations of its predicate symbol and of its tuple of arguments. In addition we give the denotation of a term as a composition of the denotations of its function symb...

We investigate algorithms for solving the satisfiability problem in composition-nominative logics of quantifier-equational level. These logics are algebra-based logics of partial predicates constructed in a semantic-syntactic style on the methodological basis, which is common with programming; they can be considered as generalizations of traditional logics on classes of partial predicates that ...

Method engineering for information system development is the discipline to construct new advanced development methods from parts of existing methods, called method fragments. To achieve this objective, we need to clarify how to mode1 the existing methods and how to assemble method fragments into new project-specific methods, so-called situational methods. Especially, to produce meaningful metho...

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlight...

This paper provides formal semantics for an extension of the ObjectRole Modeling approach that supports declaration of dynamic rules. Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves. In this paper we restrict application of dynamic rules to so-called single-step transactions, with an old state (the input of the transa...