Displacements Caused by the Temperature in Multicomponent, Multi-Layered Periodic Material Structures

Abstract

The present study aims to analyse a two-dimensional problem of displacements in theory of thermal stresses for multicomponent, multi-layered periodic composites. The model equations are obtained within the framework of the tolerance modelling procedure. These equations allow to determine the distribution of displacements caused by the temperature field in the theory of thermal stresses. The paper presents an example of a solution of a boundary value problem.

Mathematical modelling of thermoelasticity problems for thin biperiodic cylindrical shells

“…Moreover, if ε → 0 then, by means of a property of the mean value, cf. Jikov et al [2], the obtained result tends weakly to function L 0 being the averaged form of starting Lagrangian (7) under consistent asymptotic decomposition (29). Introducing the extra approximation 1 + λ/r ≈ 1, this result has the form…”

“…We can mention here monograph by Tomczyk [11] and papers by Tomczyk and Litawska [12][13][14], Tomczyk et al [15][16][17], where the length-scale effect in mechanics of periodic cylindrical shells is investigated; papers by Baron [18], where dynamic problems of medium thickness periodic plates are studied and by Marczak and Je ˛drysiak [19], Marczak [20,21], where dynamics of periodic sandwich plates is analysed; papers by Je ˛drysiak [22][23][24], which deal with stability of thin periodic plates; papers by Łaciński and Woźniak [25], Rychlewska et al [26], Ostrowski and Je ˛drysiak [27], Kubacka and Ostrowski [28], where problems of heat conduction in conductors with periodic structure are analysed. Let us also mention papers by Bagdasaryan et al [29], Tomczyk and Goła ˛bczak [30], which deal with coupled thermoelasticity problems, respectively, for multicomponent, multi-layered periodic composites and for thin cylindrical shells with microperiodic structure in circumferential direction (uniperiodic shells). The extended list of references on this subject can be found in [6][7][8][9]11].…”

Investigation and failure analysis of a diesel generator connecting rod

“…Several inspection reports on connecting rods were found to determine and make appropriate maintenance recommendations [9], [10]. In other cases, follow-up inspection of connecting rod failure was reported by hardness test, surface crack analysis, and microstructure analysis due to overheating [4], [11], [12]. Other studies on connecting rod failures have also been carried out with validation using finite element analysis (FEA) simulations.…”

Extended tolerance modelling of dynamic problems for thin uniperiodic cylindrical shells

“…We can mention here monograph by Tomczyk [10] and papers by Tomczyk et al [11,12], where the length-scale effect in mechanics of periodic cylindrical shells is investigated; papers by Baron [13], where dynamic problems of medium thickness periodic plates are studied and by Marczak and Je ˛drysiak [14], Marczak [15,16], where dynamics of periodic sandwich plates is analysed; papers by Je ˛drysiak [17][18][19], which deal with stability of thin periodic plates; papers by Łaciński and Woźniak [20], Rychlewska et al [21], Ostrowski and Je ˛drysiak [22], Kubacka and Ostrowski [23], where problems of heat conduction in conductors with periodic structure are analysed. Let us also mention papers by Bagdasaryan et al [24], Tomczyk and Goła ˛bczak [25], Tomczyk et al [26], which deal with coupled thermoelasticity problems, respectively, for multicomponent, multi-layered periodic composites, for thin cylindrical shells with micro-periodic structure in circumferential direction (uniperiodic shells) and for thin cylindrical shells with micro-periodic structure in circumferential and axial directions (biperiodic shells). The extended list of references on this subject can be found in [6][7][8][9][10].…”