Search results for "equation"
showing 10 items of 4219 documents
Set-valued and fuzzy stochastic differential equations driven by semimartingales
2013
Abstract In the paper we present set-valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties. Then we study the existence of solutions to set-valued and fuzzy-set-valued stochastic differential equations driven by semimartingales. The stability of solutions is also established.
Social Cognition and Socioecological Predictors of Home-Based Physical Activity Intentions, Planning, and Habits during the COVID-19 Pandemic
2020
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Surface effects, boundary conditions and evolution laws within second strain gradient plasticity
2014
Abstract The principle of the virtual power (PVP) is used in conjunction with the concepts of “energy residual” and “insulation condition” to address second strain gradient plasticity. The energy residual with its typical divergence format is an extra stress power playing the role of basic state variable to describe the gradient effects, whereas the insulation condition constitutes a global energy characterization of the body as part of the body/environment system. The microstructure of a second strain gradient material (but not of a first strain gradient one) is shown to exhibit surface effects with the formation of a thin boundary layer. This boundary layer is in local (and global) equili…
Constitutive equations for no-tension materials
1988
For a material which is incapable of sustaining tensile stresses (no-tension material, NTM), the local stability postulate is utilized in order to derive the appropriate equations which relate, within general 3D situations, cracking strain states and stress states to each other. Several alternative forms of these equations are discussed, either in terms of stress and strain components, or in terms of stress and strain invariants. The results obtained improve known results regarding the NTM's.
Boundary Integral Formulation for Composite Laminates in Torsion
1997
The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem's analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characte…
A nonlocal strain gradient plasticity theory for finite deformations
2009
Abstract Strain gradient plasticity for finite deformations is addressed within the framework of nonlocal continuum thermodynamics, featured by the concepts of (nonlocality) energy residual and globally simple material. The plastic strain gradient is assumed to be physically meaningful in the domain of particle isoclinic configurations (with the director vector triad constant both in space and time), whereas the objective notion of corotational gradient makes it possible to compute the plastic strain gradient in any domain of particle intermediate configurations. A phenomenological elastic–plastic constitutive model is presented, with mixed kinematic/isotropic hardening laws in the form of …
Influence of data input in the evaluation of Stress Intensity Factors from Thermoelastic Stress Analysis
2021
Abstract Thermoelastic Stress Analysis (TSA) is applied to evaluate the Stress Intensity Factor (SIF), T-stress and J-Integral in a Single-Edge-Notched-Tension sample undergoing fatigue cycling. The Williams’ series stress formulation and a least-square fitting (LSF) procedure are used to obtain the SIF and the T-stress. The evaluation is carried out with the aim to investigate the influence of the input data in the system of equations solved with the LSF, and in particular: the number of coefficients used in the Williams’ series and the choice and position of the fitted experimental data points. Three algorithms for the determination of the crack tip position are also evaluated: a coarse g…
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
Über die verzweigung des polyvinylacetats. I. Die bestimmung der übertragungskonstante des polymeren nach der methode der „α-polymeren”.
1962
Die Ubertragungskonstante (Cp) am Polymeren wird ermittelt, indem der Einflus relativ kurzkettiger „α-Polymerer” auf den Polymerisationsgrad des „α-Polymeren” gemessen und daraus Cp mit Hilfe der Reglergleichung berechnet wird. Der Polymerisationsgrad wird viskosimetrisch auf Grund der Eichmessungen von MATSUMOTO u.a. unter Berucksichtigung der Mittelwertbildung bestimmt. Aus den Messungen ergibt sich ein neuer Wert fur das Konstantenverhaltnis kab/Kw2; die Einzelwerte der Wachstums- und der Abbruchskonstante liegen danach erheblich hoher als bisher angenommen wurde. Fur Cp ergibt sich (2,5 ± 0,5)·10−4 in guter Ubereinstimmung mit entsprechenden Mesergebnissen an niedermolekularen Modellsub…