scholarly journals The sustainability of micropolar concrete plasticity model to the finite element size

Vestnik MGSU ◽  
2019 ◽  
pp. 559-569
Author(s):  
Olga N. Pertseva ◽  
Gleb V. Martynov ◽  
Daria E. Monastyreva ◽  
Ekaterina I. Pereladova ◽  
Zaur S. Daurov ◽  
...  
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Main Crack ◽  
Maximum Load ◽  
Beam Model ◽  
Element Mesh ◽  
Linear Elastic ◽  
Second Stage ◽  
Element Size ◽  
Micro Cracks

Introduction. As it is known, deformation of concrete can be divided into several stages. The first stage is characterized by a linear dependence of deformations and stresses, elastic deformations and small loads that, as they increase, lead to the second stage. At the second stage, the dependence becomes curvilinear, while deformations are irreversible, since micro-cracks are formed. Further consolidation of the micro-cracks into meso- and main cracks refers to the third stage and is accompanied by a redistribution of energy to the area of the main crack mouth. However, reaching the ultimate strength is not accompanied by an instant loss of bearing capacity due to the effect of decompression. This phenomenon should be taken into account in the numerical simulation of concrete and reinforced concrete structures, because it significantly affects their strength characteristics. The introduction of such a refinement in the design models will allow reducing cross-sections of the construction components and accordingly getting rid of material overruns. Materials and methods. A digital sample is created for the study using the ANSYS software. A beam model is simulated as a single-span beam with longitudinal reinforcement in the bending zone. The load is applied as a 70 mm offset to the nodes in the line along the application point. Reinforcement is simulated as bilinear isotropic strengthening elements (LINK180). For uniform load distribution, load plates with linear elastic properties are specified at the points where boundary conditions and load are applied. Results. According to the obtained data, stress-deformation curves are constructed identically to the concrete deformation diagram. The values of loads when the first cracking occurs (end of the linear-elastic state), peak loads when the main crack is formed (maximum load for the unreinforced case and the beginning of the steel softening for the reinforced case) as well as ultimate loads and maximum deflections at the mid-span are compared. Conclusions. The results give insignificant (up to 5 %) discrepancies when changing the finite element size. Therefore, when working with calculation software, developers will be able to create correct models with any spacing of the finite element mesh depending on the available computational capabilities. Micropolar theory for simulating the concrete decompression can be considered sustainable to the size of the finite elements.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Development of a New Artificial Knee Joint for an Asian and Middle Eastern Population

2013 ◽  
Author(s):  
Harcharan Singh Ranu
Keyword(s):  
Finite Element ◽  
Body Weight ◽  
Maximum Load ◽  
The Body ◽  
The Other ◽  
Elastic Behavior ◽  
Loading Conditions ◽  
Load Bearing Capacity ◽  
Linear Elastic ◽  
Materials Used

Design of an artificial knee was developed using computer 3-D modeling, the high flexion knee was obtained by using a multi-radii design pattern, The increase of final 20 degrees in flexion was obtained by increasing the condylar radii of curvature. The model of the high flexion knee was developed and one of the models was subjected to finite element modeling and analysis. The compositions of components in the artificial knee were, femoral component and the tibial component were metal, whereas the patellar component and the meniscal insert were made using polyethylene. The metal component used for the analysis in this study was Ti6Al4V and the polyethylene used was UHMWPE. Overall biomaterials chosen were: meniscus (UHMWPE, mass = 0.0183701 kg, volume = 1.97518e-005 m3), tibial component (Ti6Al4V, mass = 0.0584655 kg, volume = 1.32013e-005 m3), femoral component (Ti6Al4V, mass = 0.153122 kg, volume = 3.45742e-005 m3), total artificial assembly (mass = 0.229958 kg, volume = 6.75e-005m3). However, in this design the load had been taken to 10 times the body weight. The weight over single knee is only half the maximum load as the load is shared between the two knee joints. Following were the loading conditions, taking average body weight to be 70Kgs and taking extreme loading conditions of up to 10 times the body weight, i.e. 700Kgs on each of the leg performed the Finite Element Analysis (FEA) over the newly designed knee. The loading was done at an increment of 100 Kgs. The loading conditions and the meshing details for the analysis of the assembly were Jacobian check: 4 points, element size: 0.40735 cm, tolerance: 0.20367 cm, quality: high, number of elements: 80909, number of nodes: 126898. A maximum load of 600 Kgs is optimum for this model. The other components observed linear elastic behavior for the applied loads. Based on these results it was determined that the load bearing capacity of the model were well within the failure levels of the materials used for the analysis. A maximum load of 600 Kgs is optimum for this model. The other components observed linear elastic behavior for the applied loads. Based on these results it was determined that the load bearing capacity of the model were well within the failure levels of the materials used for the analysis. Conclusion drawn from this is that for the first time an innovative new design of an artificial knee joint to suite a segment of some religious population has been developed. This allows them to pray, bend in different positions and squat without too much difficulty.

scholarly journals BEAM ELEMENT UNDER FINITE ROTATIONS

2021 ◽  
Vol 30 ◽  
pp. 87-92
Author(s):  
Emma La Malfa Ribolla ◽  
Milan Jirásek ◽  
Martin Horák
Keyword(s):  
Cross Sections ◽  
Shooting Method ◽  
Small Strain ◽  
Beam Model ◽  
Equilibrium Equations ◽  
Finite Rotations ◽  
Nonlinear Beam ◽  
Linear Elastic ◽  
Beam Elements ◽  
Large Rotations

The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law.The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

A Measure for the Fracture Toughness of Cement Based Materials

1984 ◽  
Vol 42 ◽  
Author(s):  
Y. S. Jenq ◽  
S. P. Shah
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Direct Method ◽  
Maximum Load ◽  
Nonlinear Finite Element ◽  
Linear Elastic ◽  
Cement Based Materials ◽  
Notch Length ◽  
Elastic Fracture ◽  
A Direct Method

It is frequently reported that the higher the strength of cement based materials, the more brittle is their behavior. It could he useful to quantitatively express the degree of brittleness. Many attempts [1–13] have been made to use linear elastic fracture mechanis (LEFM) to quantitatively express the degree of brittleness. For example, by testing notched beams one can calculate, using the formulas developed from LEFM, a quantity called fracture toughness and termed KIC from the measured maximum load and the initial notch-length. Unfortunalely, it has been observed that K thus calculated is dependent on the dimension of the beams. Many researchers have attempted to analyze this size dependency. Such approaches are usually quite cumbersome and are often based on expensive nonlinear finite element programs. In this paper a direct method is suggested to calculate two size-independent fracture toughness parameters from the experimental results. The method was developed based on tests on notched-beams of different mix proportions and different sizes.

Accurate Prediction of Strains and Stresses in 2-D Elasticity Using Adini’s Finite Element

2015 ◽  
Author(s):  
Donovan A. Aguirre-Rivas ◽  
Karim H. Muci-Küchler
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Finite Element Solution ◽  
Element Solution ◽  
Time Step ◽  
Solution Approach ◽  
Linear Elastic ◽  
Element Size ◽  
Linearized Problem

In the interest of obtaining accurate stress predictions in linear elastic problems while keeping the computational cost low, a finite element solution approach using cubic elements that include not only the displacement but also the spatial derivatives of the displacement as nodal degrees of freedom (DOFs) is explored in this paper. The proposed approach has the advantage that the nodal values of the strains, and hence the stresses, can be directly computed from the finite element solution and, as shown in this paper, it is capable of converging faster to the analytical solution than the commonly used reduced integration Serendipity quadratic element. Because the proposed approach is capable of achieving high accuracy using less DOFs, it is possible to use coarser meshes than with conventional elements. This is of particular importance in dynamic problems in which explicit techniques are used and the size of the time step is tied to the element size. Moreover, the proposed approach can be beneficial in non-linear problems in which stepping techniques are used to solve a linearized problem and the strains or stresses of the current step are used as input for the following step.

scholarly journals Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

2018 ◽  
Vol 68 (2) ◽  
pp. 35-52
Author(s):  
Justín Murín ◽  
Mehdi Aminbaghai ◽  
Vladimír Goga ◽  
Vladimír Kutiš ◽  
Juraj Paulech ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Twist Angle ◽  
Additional Degree ◽  
Linear Elastic ◽  
Solid Finite Elements ◽  
Stress And Deformation

AbstractIn this paper, results of numerical simulations and measurements are presented concerning the non-uniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linear-elastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results.

scholarly journals Homogenization and Equivalent Beam Model for Fiber-Reinforced Tubular Profiles

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2069
Author(s):  
Daniel Gnoli ◽  
Sajjad Babamohammadi ◽  
Nicholas Fantuzzi
Keyword(s):  
Finite Element ◽  
Hollow Cylinder ◽  
Cross Sections ◽  
Laminated Composite ◽  
Beam Theory ◽  
Material Design ◽  
Composite Beams ◽  
Beam Model ◽  
2D And 3D ◽  
Euler Bernoulli Beam

The current work presents a study on hollow cylinder composite beams, since hollow cylinder cross-sections are one of the principal geometry in many engineering fields. In particular, the present study considers the use of these profiles for scaffold design in offshore engineering. Composite beams cannot be treated as isotropic ones due to couplings mainly present among traction, torsion, bending and shear coefficients. This research aims to present a simple approach to study composite beams as they behave like isotropic ones by removing most complexities related to composite material design (e.g., avoid the use of 2D and 3D finite element modeling). The work aims to obtain the stiffness matrix of the equivalent beam through an analytical approach which is valid for most of the laminated composite configurations present in engineering applications. The 3D Euler–Bernoulli beam theory is considered for obtaining the correspondent isotropic elastic coefficients. The outcomes show that negligible errors occur for some equivalent composite configurations by allowing designers to continue using commercial finite element codes that implement the classical isotropic beam model.

Elastic-Plastic Finite Element Stress Analysis of a Carburized Shaft With Spatial Gradient in Mechanical Properties

2006 ◽  
Author(s):  
Patrick A. Tibbits
Keyword(s):  
Finite Element ◽  
High Hardness ◽  
Spatial Gradient ◽  
Element Mesh ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
The Core ◽  
Bending Load ◽  
Core Hardness ◽  
Outside Diameter

Low core hardness in a carburized bicycle pedal shaft allows yielding in the core region when the shaft carries a bending load. Quantitatively evaluating the effect of core hardness level requires simulation of the gradient in material properties from the high-hardness thin outer case to the low-hardness core. This study develops a scheme for generating a high-resolution finite element mesh near the outside diameter of the shaft, coupled with a method for specifying elastic-plastic stress-strain curves which vary with depth below the carburized surface. The method enables examination of the stress localization and intensification in the case when yielding occurs in the core. The results show the insufficiency of the linear elastic assumption, and explain failures of shafts with anomalously low core hardness.

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