Auswahl der wissenschaftlichen Literatur zum Thema „32-node solid element“

The aim of the study described in this paper is to assess the effect of forces acting on the tube sheet during friction welding on the stress-strain state of the tube sheet.For this, we calculated the stresses and displacements arising in the tube sheet during friction welding. The calculations were carried out in the ANSYS (finite element analysis software package). To carry out the calculations, solid-state models of tube sheets with diameters of 400, 600, 800, 1000, 1200, 1400 mm and thicknesses of 30, 40, 50, 60, 70 mm were created. The diameter of the holes for the heat exchange tubes was chosen equal to 25 mm, the holes are placed on the vertices of an equilateral triangle with a step equal to 32 mm. Then, based on geometric models, grids of 8-node finite elements were created. The calculation model takes into account the symmetry of the geometric model and the character of loading relative to the YZ and XZ planes. The material used was steel with a Poisson's ratio of 0.3 and an elastic modulus of 2,11·105 MPa.As a result of the calculations, it was found that as a result of the action of force factors during friction welding, significant stresses and deformations arise in the tube sheet. The greatest values of deflection and stresses occur in the central sector of the tube sheet in the area of application of force. In this case, the zone of maximum stresses is significantly localized: they are concentrated around the central hole, and movements smoothly increase from the periphery to the center of the tube sheet.The value of this study is that it allowed to determine the need to use special equipment that increases the local stiffness of the tube sheet sector subjected to friction welding.

The node-based smoothed finite element method (NS-FEM) has been recently proposed by Liu et al to enhance the computational effect for solid mechanics problems. However, it is evident that the NS-FEM behaves "overly-soft" and so it may lead to instability for dynamic problems. The instability can be clearly shown as spurious non-zero energy modes in free vibration analysis. In this paper, we present a stabilization of the node-based smoothed finite element method (SN-FEM) that is stable (no spurious non-zero energy modes) and more effective than the standard finite element method (FEM). Three numerical illustrations are given to evince the high reliability of the proposed formulation.

An alpha finite element method (\(\alpha\)FEM) has been recently proposed to compute nearly exact solution in strain energy for solid mechanics problems using three-node triangular (\(\alpha\)FEM-T3) and four-node tetrahedral (\(\alpha\)FEM-T4) elements. In the \(\alpha\)FEM, a scale factor \(\alpha \in [0, 1]\) is used to combine the standard fully compatible model of the FEM with a quasi-equilibrium model of the node-based smoothed FEM (NS-FEM). This novel combination of the FEM and NS-FEM makes the best use of the upper bound property of the NS-FEM and the lower bound property of the standard FEM. This paper concentrates on applying directly the \(\alpha\)FEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using \(\alpha = 0.6\) for 2D problems and \(\alpha = 0.7\) for 3D problems.

Солидные псевдопапиллярные опухоли поджелудочной железы (СПО) представляют собой высокодифференцированные потенциально злокачественные опухоли экзокринной части поджелудочной железы, состоящие из гомогенных эпителиальных клеток с солидно-кистозными элементами. СПО чаще поражают молодых женщин, локализуются в основном в теле и хвосте (67%), головке (32%) поджелудочной железы. Развитие СПО протекает бессимптомно до тех пор, пока опухоли не увеличиваются в размере настолько, что инфильтрируют окружающие ткани, вовлекают в процесс печень, брюшину, метастазируют в отдаленные органы, такие как легкие. Было продемонстрировано, что, несмотря на их злокачественный потенциал, R0 и хирургическая резекция единым блоком увеличивают общую выживаемость и выживаемость без признаков заболевания. Хирургическая техника удаления СПО зависит от локализации опухоли. После хирургического лечения 5-летняя выживаемость составляет до 97%, что является хорошим прогнозом. Расширенная лимфодиссекция не считается необходимой из-за низкого риска метастазирования СПО в лимфатические узлы. Для регистрации возможных поздних рецидивов рекомендуется длительное наблюдение. Solid pseudopapillary tumours of the pancreas (SPTs) are low-grade malignant potential tumors of the exocrine pancreas comprised of homogeneous, poorly adherent epithelial cells with solid-cystic elements. SPN mostly affects young females, the tumour mainly located in the body and tail of the pancreas (67%) and the head (32%). SPTs are asymptomatic until they get large and are found to be locally aggressive and infiltrate surrounding tissues, metastatic spread to the liver, peritoneum, and distant organs such as the lungs are detected. Despite of their malignancy, R0 and en bloc surgical resection have been demonstrated to enhance overall survival and disease-free survival. The surgical technique for SPTs is influenced by the location of the tumour. An excellent prognosis with a 5-year survival rate of up to 97% after surgical excision. Significant lymphadenectomy is not considered required because of the low risk of lymph node metastases of such tumor cells. Late recurrences have been recorded; long-term surveillance is recommended.

Les structures multicouches en bois, assemblées par des goujons en bois densifié, constituent une solution durable et innovante pour le secteur de la construction. Le développement de modèles prédictifs par éléments finis nécessite une représentation volumique de la géométrie pour modéliser le comportement mécanique complexe de ces structures. Cependant, les modèles volumiques sont couteux, notamment dans le cadre des études de variabilité et d’optimisation. Dans cette thèse, des approches de types volumique, volume-coque et volume-poutre, sont développées pour obtenir des modèles précis et qui peuvent être qualifiés de juste nécessaires. L’étude du comportement mécanique des structures multicouches en bois révèle que les lamelles adoptent un comportement de coque tandis que les goujons se comportent comme des poutres. Des champs de déplacement d’ordre supérieur dans l’épaisseur des lamelles et dans la section des goujons sont identifiés. Pour respecter ces champs de déplacement tout en gardant une représentation volumique, deux méthodes ont été développées. Une première méthode exploite des éléments volumiques standards en appliquant des théories de coque à travers l’épaisseur des lamelles et des théories de poutre à travers les sections des goujons. Une seconde méthode exploite un élément hexaédrique à 32 nœuds et s’inspire des principes des éléments volume-coque et volume-poutre, avec un seul élément dans l’épaisseur des lamelles et un seul élément dans la section des goujons. Les résultats démontrent que les méthodes proposées dans cette thèse mènent à des outils de modélisation efficaces pour les structures multicouches en bois assemblées par des goujons en bois densifié. Ces méthodes ouvrent également de nouvelles pistes de développements futurs et des perspectives d’application à d’autres types de structures
Multilayered timber structures, assembled using densified wood dowels, represent a sustainable and innovative solution for the construction sector. The development of predictive finite element models requires a solid representation of the geometry for modelling the complex mechanical behaviour of these structures. However, solid models are costly, especially in the context of variability studies and optimization. In this thesis, solid, solid-shell, and solid-beam approaches are developed to obtain accurate models that can be considered as the best compromise. The study of the mechanical behaviour of multilayered timber structures reveals that the layers adopt a shell-like behaviour, while the dowels behave like beams. Higher-order displacement fields through the thickness of the layers and through the cross-section of the dowels are identified. To meet these displacement fields while maintaining a solid representation, two methods have been developed. A first method exploits standard solid elements by applying shell theories through the thickness of the layers and beam theories through the sections of the dowels. A second method uses a 32-node hexahedral element and is inspired by the principle of solid-shell and solid-beam elements, with a single element through the thickness of the layers and a single element through the section of the dowels. The results demonstrate that the methods proposed in this thesis lead to effective modelling tools for multilayered timber structures assembled with densified wood dowels. These methods offer perspectives for future developments and applications to other types of structures

In most finite-element-analysis codes, accuracy is achieved through the use of the hexahedron hexa-20 elements (a node at each of the 8 corners and 12 edges of a brick element). Unfortunately, without an additional node in the center of each of the element’s 6 faces, nor in the center of the hexa, the hexa-20 elements are not fully quadratic such that its truncation error remains at h2(0), the same as the error of a hexa-8 element formulation. To achieve an accuracy with a truncation error of h3(0), we need the fully-quadratic hexa-27 formulation. A competitor of the hexa-27 element in the early days was the so-called serendipity cubic hexa-32 solid elements (see Ahmad, Irons, and Zienkiewicz, Int. J. Numer. Methods in Eng., 2:419–451 (1970) [1]). The hexa-32 elements, unfortunately, also suffer from the same lack of accuracy syndrome as the hexa20’s. In this paper, we investigate the accuracy of various elements described in the literature including the fully quadratic hexa-27 elements to a shell problem of interest to the pressure vessels and piping community, viz. the shell-element-based analysis of a barrel vault. Significance of the highly accurate hexa-27 formulation and a comparison of its results with similar solutions using ABAQUS hexa-8, and hexa-20 elements, are presented and discussed. Guidelines are proposed for selection of better elements.

In most finite-element-analysis codes, accuracy is achieved through the use of the hexahedron hexa-20 elements (a node at each of the 8 corners and 12 edges of a brick element). Unfortunately, without an additional node in the center of each of the element’s 6 faces, nor in the center of the hexa, the hexa-20 elements are not fully quadratic such that its truncation error remains at h(0), the same as the error of a hexa-8 element formulation. To achieve an accuracy with a truncation error of h3(0), we need the fully-quadratic hexa-27 formulation. A competitor of the hexa-27 element in the early days was the so-called serendipity cubic hexa-32 solid elements (see Ahmad, Irons, and Zienkiewicz, Int. J. Numer. Methods in Eng., 2:419-451 (1970) [1]). The hexa-32 elements, unfortunately, also suffer from the same lack of accuracy syndrome as the hexa20’s. In recent work, we have developed methods to test the errors and the rate of convergence in FEA [2,3,4]. In this paper, we propose a new metric for determining the quality of isoparametric elements a priori. Significance of the highly accurate hexa-27 formulation and a comparison of its results with similar solutions using ABAQUS hexa-20 elements, are presented and discussed. Guidelines are proposed for selection of better elements.