A simple finite element for elastic-plastic deformations of shells

1982 ◽  
Vol 34 (1-3) ◽  
pp. 1051-1064 ◽  
Author(s):  
Demosthenes Talaslidis ◽  
Gerald Wempner
Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 39
Author(s):  
Łukasz Warguła ◽  
Dominik Wojtkowiak ◽  
Mateusz Kukla ◽  
Krzysztof Talaśka

This article presents the results of experimental research on the mechanical properties of pine wood (Pinus L. Sp. Pl. 1000. 1753). In the course of the research process, stress-strain curves were determined for cases of tensile, compression and shear of standardized shapes samples. The collected data set was used to determine several material constants such as: modulus of elasticity, shear modulus or yield point. The aim of the research was to determine the material properties necessary to develop the model used in the finite element analysis (FEM), which demonstrates the symmetrical nature of the stress distribution in the sample. This model will be used to analyze the process of grinding wood base materials in terms of the peak cutting force estimation and the tool geometry influence determination. The main purpose of the developed model will be to determine the maximum stress value necessary to estimate the destructive force for the tested wood sample. The tests were carried out for timber of around 8.74% and 19.9% moisture content (MC). Significant differences were found between the mechanical properties of wood depending on moisture content and the direction of the applied force depending on the arrangement of wood fibers. Unlike other studies in the literature, this one relates to all three stress states (tensile, compression and shear) in all significant directions (anatomical). To verify the usability of the determined mechanical parameters of wood, all three strength tests (tensile, compression and shear) were mapped in the FEM analysis. The accuracy of the model in determining the maximum destructive force of the material is equal to the average 8% (for tensile testing 14%, compression 2.5%, shear 6.5%), while the average coverage of the FEM characteristic with the results of the strength test in the field of elastic-plastic deformations with the adopted ±15% error overlap on average by about 77%. The analyses were performed in the ABAQUS/Standard 2020 program in the field of elastic-plastic deformations. Research with the use of numerical models after extension with a damage model will enable the design of energy-saving and durable grinding machines.


Vestnik MGSU ◽  
2021 ◽  
pp. 294-305
Author(s):  
Evgeny A. Moiseichik ◽  
Yuri V. Vasilevich ◽  
Aliaksandr E. Moiseichik ◽  
Aliaksei M. Yaznevich ◽  
Aliaksandr A. Yakauleu

Introduction. In the transverse and longitudinal sections of the rods with a periodic profile, there are layers with different structural and phase states, physical and mechanical characteristics, stress state and resistance to external influences. The appearance of plastic deformations in the bases of the depressions and other defects of a periodic profile during stre­tching of the rods leads to a decrease in the resistance to corrosion damage due to the occurrence of galvanic pairs between inhomogeneous sections of the rod. This makes the computational and experimental studies of the deformed state of such rods under tension urgent. Materials and methods. The finite element modeling of the deformation process during the elastic-plastic work of steel was carried out using the ANSYS software complex and solid models of the rods under study. Experimental tests of the samples were carried out using an R-50 tensile testing machine with the recording of a load-elongation diagram in accordance with the requirements of GOST 1497. The process of deformation of the samples was displayed by photographic recording. After the destruction of the samples, the geometric dimensions (lengths, changes in cross-sections) were measured, the typical types of samples and their fragments, and fractures were photographed. Results. On experimental and finite-element models, it was found that during elastic-plastic deformation of steel rods in dangerous sections, a change in the angle of inclination of the banks of periodic protrusions (undercuts) affects the volume of plastically deformable material at the base of the undercuts. Such an analysis of the models in the limiting state has shown that the volume of the plastically deformed material is significantly reduced at the angles of the protrusions at their bases with the axis of the rod close to 900. The calculation established that the plastically deformed area at the base of sharp undercuts is more than a hundred times smaller than the corresponding volume at the base of the gently sloping undercuts. In samples with a group of protrusions, constraint of plastic deformations at the base occurs only for protrusions, the width of which is comparable to the diameter of the rod in weakened sections. The greatest development of equivalent plastic deformations is observed at the base between narrow projections. Damage to the outer layers of quasi-composite rods with a periodic profile causes significant changes in the stress-strain state of the rods under tension. Conclusions. The finite element modeling of the tensile work of steel rods with a periodic profile with a quasi-composite structure is a complex multifactorial problem. Plastic deformations develop in the depressions of the periodic profile. At the same time, undeformed areas remain in the metal of the protrusions. These zones have different potentials and between them the occurrence of internal galvanic currents is possible, leading to the acceleration of corrosion processes.


2020 ◽  
Vol 17 ◽  
pp. 00199
Author(s):  
Arsen Dzhabrailov ◽  
Anatoly Nikolaev ◽  
Natalya Gureeva

The article describes an algorithm for calculating an axisymmetrically loaded shell structure with a branching meridian, taking into account elastic-plastic deformations when loading based on the deformation theory of plasticity without assuming that the material is incompressible during plastic deformations. The correct relations which determine the static conjugation conditions of several revolution shells in the joint assembly are used. A comparative analysis of finite element solutions is presented for various options plasticity matrix development at the loading stage.


Author(s):  
Ali Sepehri ◽  
Kambiz Farhang

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Multiscale modeling of the elastic-plastic rough surface contact is presented in which asperity-level FE-based constitutive relations are statistically summed to obtain total force in the normal and tangential direction. The equations derived are in the form of integral functions and provide expectation of contact force components between two rough surfaces. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.


Author(s):  
K. M. Prabhakaran ◽  
S. R. Bhate ◽  
V. Bhasin ◽  
A. K. Ghosh

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires evaluation of J-integral. The J-integral values for elbows with axial part-through internal crack at crown under in-plane bending moment are limited in open literature. This paper presents the J-integral results of a thick and thin, 90-degree, long radius elbow subjected to in-plane opening bending moment based on number of finite element analyses covering different crack configurations. The non-linear elastic-plastic finite element analyses were performed using WARP3D software. Both geometrical and material nonlinearity were considered in the study. The geometry considered were for Rm/t = 5, and 12 with ratio of crack depth to wall thickness, a/t = 0.15, 0.25, 0.5 and 0.75 and ratio of crack length to crack depth, 2c/a = 6, 8, 10 and 12.


Author(s):  
A. Ajdari ◽  
P. K. Canavan ◽  
H. Nayeb-Hashemi ◽  
G. Warner

Three-dimensional structure of trabecular bone can be modeled by 2D or 3D Voronoi structure. The effect of missing cell walls on the mechanical properties of 2D honeycombs is a first step towards understanding the effect of local bone resorption due to osteoporosis. In patients with osteoporosis, bone mass is lost first by thinning and then by resorption of the trabeculae [1]. Furthermore, creep response is important to analyze in cellular solids when the temperature is high relative to the melting temperature. For trabecular bone, as body temperature (38 °C) is close to the denaturation temperature of collagen (52 °C), trabecular bone creeps [1]. Over the half of the osteoporotic vertebral fractures that occur in the elderly, are the result of the creep and fatigue loading associated with the activities of daily living [2]. The objective of this work is to understand the effect of missing walls and filled cells on elastic-plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis. The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the structure decreased by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials.


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