Dual and mixed nonsymmetric stress-based variational formulations for coupled thermoelastodynamics with second sound effect

Evolution and Modern Approaches of the Power Transformer Cost Optimization Methods

“…Due to the increased accuracy, the appropriate solution of the different physical fields leads to solve elliptic integrals, second order Bessel-functions etc. These partial differential equations can be solved by numerical methods in reasonable time and accuracy [1,[82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101].…”

Dual-mixed hp-version axisymmetric shell finite element using NURBS mid-surface interpolation

“…(61), (63)- (64), and (66) expressed in terms of the stress coefficients 0σ 11 , 0σ 22 , 0σ 33 , 1σ 11 , 1σ 22 , and 0σ 31 describe the bending-shearing-and the extension-compression problems of the axisymmetric shell, while Eqs. (62) and (65) given in terms of the stress coefficients 0σ 21 , 0σ 32 , 1σ 21 describe its torsional problem. It can easily be proven for axisymmetric problems of shells of revolution that the bending-shearing equations (including tension-compression) are decoupled from the torsional equations.…”

“…Based on the computational experiments and the theoretical background, it is worth further developing the presented hp-version shell FE for (i) more general initial-BVPs (contact and dynamic problems) of shells [61,62], (ii) modeling the mechanical behavior of layered structures (composites) with extremely thin or moderately thick layers, taking into account the slip between them, (iii) automatic hp-adaptivity, applying the error indicators introduced, for example, in [8,20,39], (iv) coupled thermoelasticity and thermoelectroelasticity problems, using the code Artap for FE mesh optimization [41][42][43] and (v) 2D axisymmetric shell problems. This latter extension allows us to analyze more general BCs.…”

“…The difficulties arise from the complexity of the theoretical background and the selection of the appropriate (stable) polynomial approximation space for the independent variables. The aforementioned procedure results in a three-field DM variational formulation; see the detailed descriptions, for instance, in [50,61,62]. This idea was originally suggested in [18].…”

“…In accordance with the above particularized computational difficulties and research directions for their avoidance, the main aim of this paper is the construction of a locking-free and robust (uniformly stable) dual-and mixed axisymmetric hp-shell FE, which later can be extended to more complicated, coupled initialboundary value problems of elastic shells (see, for example, in [61,62]). Throughout the paper, the indicial notation of tensors and the usual summation convention is used.…”