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 The Generalized Constitutive Law in Nonlinear Structural Analysis of Steel Frames

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Reference Model ◽  
Constitutive Models ◽  
Shear Stiffness ◽  
Beam Element ◽  
Linear Analysis ◽  
Constitutive Law ◽  
Complex Materials ◽  
Shear Forces ◽  
Beam Structures ◽  
Numerical Examples

The article presents a modified finite element (FE) based algorithm for nonlinear analysis of 2D beam structures, which takes into account the influence of the shear forces. The method proposed enables using complex materials with nonlinearities without the need of implementing advanced constitutive models in FE routines. It can be directly integrated with commonly available FE software for linear analysis of beam structures, so its functionality can be easily extended also with material nonlinearities. The presented approach adopts the generalized constitutive law algorithm to iteratively modify the stiffness of beam element. To address an influence of a shear stiffness, a Timoshenko beam element was used. The methodology was implemented and its performance was verified on several numerical examples. For validation, the displacements and the ultimate loads were compared with the values from a commercial FE software. The results shown a good correlation between the reference model and the method proposed.

scholarly journals Application of the Generalized Nonlinear Constitutive Law to Hollow-Core Slabs

2021 ◽  
Author(s):  
Natalia Staszak ◽  
Tomasz Garbowski ◽  
Barbara Ksit
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Crack Opening ◽  
Constitutive Law ◽  
Fe Model ◽  
Hollow Core ◽  
Linear Finite Element ◽  
Deformation State ◽  
Non Linear ◽  
Nonlinear Constitutive Law

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

Compliant assembly analysis including initial deviations and geometric nonlinearity—Part I: Beam structure

2018 ◽  
Vol 233 (12) ◽  
pp. 4233-4246
Author(s):  
Tao Liu ◽  
Zhi-Min Li ◽  
Sun Jin ◽  
Wei Chen
Keyword(s):  
Geometric Nonlinearity ◽  
Large Scale ◽  
Virtual Work ◽  
Flexible Beam ◽  
Beam Model ◽  
Analysis Method ◽  
Variation Analysis ◽  
Beam Structures ◽  
Compliant Assembly ◽  
Assembly Analysis

In the past decades, several compliant assembly analysis models have been developed to consider structural deformations during assembly progresses. Available methods address the influence of linear elastic deformations, whereas for the case of large-scale flexible structures with complex boundary conditions, the geometric nonlinearity will be a significant factor affecting the accuracy of assembly variation prediction. This paper introduces a refined mechanical model to develop a variation analysis method for beam structures. Based on the Timoshenko theory, governing equations of flexible beam are obtained by using the principle of virtual work with consideration of initial deviations and a von Kármán type of kinematic nonlinearity. Moreover, corresponding finite element formulas are presented, which also can be degenerated into non-initial deviation form or the linearized form. With the nonlinear beam model, an assembly variation analysis method is proposed for beam structures, which takes initial deviations, fixture errors, and matching deviations into account. Case studies of static loading analysis and slender beam assembly springback analysis are demonstrated to verify the feasibility and accuracy of the presented method.

Real-Time Structure Shape Estimation Using Distributed Fiber Bragg Grating Sensors

2009 ◽  
Author(s):  
Hong-Il Kim ◽  
Lae-Hyong Kang ◽  
Jae-Hung Han
Keyword(s):  
Real Time ◽  
High Speed ◽  
Estimation Method ◽  
Time Estimation ◽  
Flexible Beam ◽  
Beam Model ◽  
Shape Estimation ◽  
Rotating Beam ◽  
Structural Shape ◽  
Beam Structures

One of the emerging issues in lightweight aerospace structures is the real-time estimation of the structural shape changes. In order to reconstruct the structure shape based on the measured strain data at multiple points, the displacement-strain transformation (DST) method has been used. In this study, simulation for a 1-D beam model was performed to verify the DST method. Bending displacements for various excitation conditions were successfully estimated using the simulated strain signals. Strain sensor positions were optimized by the minimization of the condition number of the DST matrix for the 1-D beam. We further expanded the shape estimation method to rotating beams. A rotating flexible beam experimental model was constructed and a numerical simulation model was also prepared. Multiplexed four FBG sensors were fabricated and attached to the rotating beam structures to measure strains at four different locations. The experimental device has an optical rotary coupler, and the sensor signals are transmitted through the optical rotary coupler. Bending displacements were estimated based on the FBG signals and compared with directly measured displacement data using photographs taken by a high-speed camera. This shows the validity of the proposed shape estimation technique based on DST matrix for rotating beam structures.

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 Generalized Nonlinear Constitutive Law Applied to Steel Trapezoidal Sheet Plates

2021 ◽  
Author(s):  
Natalia Staszak ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Nonlinear Finite Element ◽  
Constitutive Law ◽  
Shell Structures ◽  
Nonlinear Material ◽  
Nonlinear Finite Element Method ◽  
Nonlinear Materials ◽  
Nonlinear Constitutive Law

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

A Multi-Scale Approach to the Analysis of Ultra Deepwater Unbonded Flexible Risers

2009 ◽  
Author(s):  
Ali Bahtui ◽  
Giulio Alfano ◽  
Hamid Bahai
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Element Model ◽  
Constitutive Law ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Multi Scale ◽  
Non Linear ◽  
Euler Bernoulli Beam

The results of a detailed, non-linear finite-element analysis of a small-scale (i.e. 1.7m long) six-layer unbonded flexible riser, accounting for interlayer contact and frictional slip, are used to calibrate a novel, simplified constitutive model for a 3D, non-linear Euler-Bernoulli beam model suitable for large scale analyses (hundreds of meters in length where water depth is more than 1000m). The detailed finite element model contains all the layers, each modeled separately with contact interfaces between them. The finite element model includes the main features of the riser geometry with very little simplifying assumptions made. The detailed finite element model is formulated in the framework of a novel, multi-scale approach potentially suitable for ultra deepwater applications. A simple, three-dimensional Euler-Bernoulli beam element, suitable for large scale analyses, is developed based on a non-linear constitutive law for the beam cross-section relating bending curvatures to the conjugate stress resultants.

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.

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