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A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loadingPublikacja
The main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three...
We consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
Mixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based onthe three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotationfields, both strain and stress resultant fields are treated as independent. The elements are derived in the frame-work of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells.The...
The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic...
Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patchesPublikacja
This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite...
Pantographic metamaterials: an example of mathematically driven design and of its technological challengesPublikacja
In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...
The paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
Paper presents the application of the Cosserat rod theory and newly developed associated finite elements code as the tools that support in the expert-designing engineering practice. Mechanical principles of the 3D spatially curved rods, dynamics (statics) laws, principle of virtual work are discussed. Corresponding FEM approach with interpolation and accumulation techniques of state variables are shown that enable the formulation...
In this paper, we demonstrate a method for self-organization and leader following of nonholonomic robotic swarm based on spring damper mesh. By self-organization of swarm robots we mean the emergence of order in a swarm as the result of interactions among the single robots. In other words the self-organization of swarm robots mimics some natural behavior of social animals like ants among others. The dynamics of two-wheel robot...
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