scholarly journals Buckling of Planar Micro-Structured Beams

2020 ◽  
Vol 10 (18) ◽  
pp. 6506 ◽  
Author(s):  
Manuel Ferretti ◽  
Francesco D’Annibale
Keyword(s):  
Constitutive Relations ◽  
Constitutive Law ◽  
Equivalent Model ◽  
Square Lattice ◽  
Beam Model ◽  
Micro Structure ◽  
Buckling Behavior ◽  
Energy Equivalence ◽  
Homogenization Approach ◽  
A Cell

In this paper, a Timoshenko beam model is formulated for buckling analysis of periodic micro-structured beams, uniformly compressed. These are planar grid beams, whose micro-structure consists of a square lattice of equal fibers, modeled as Timoshenko micro-beams. The equivalent beam model is derived in the framework of a direct one-dimensional approach and its constitutive law, including the effect of prestress of the longitudinal fibers, is deduced through a homogenization approach. Accordingly, micro–macro constitutive relations are obtained through an energy equivalence between a cell of the periodic model and a segment of the equivalent beam. The model also accounts for warping of the micro-structure, via the introduction of elastic and geometric corrective factors of the constitutive coefficients. A survey of the buckling behavior of sample grid beams is presented to validate the effectiveness and limits of the equivalent model. To this purpose, results supplied by the exact analyses of the equivalent beam are compared with those given by finite element models of bi-dimensional frames.

scholarly journals Static and Dynamic Responses of Micro-Structured Beams

2020 ◽  
Vol 10 (19) ◽  
pp. 6836
Author(s):  
Francesco D’Annibale ◽  
Manuel Ferretti ◽  
Angelo Luongo
Keyword(s):  
Three Dimensional ◽  
Constitutive Law ◽  
Dynamic Responses ◽  
Equivalent Model ◽  
Beam Model ◽  
Timoshenko Model ◽  
3D Space ◽  
Energy Equivalence ◽  
A Cell ◽  
The Masses

In this study, we developed a one-dimensional Timoshenko beam model, embedded in a 3D space for static and dynamic analyses of beam-like structures. These are grid cylinders, that is, micro-structured bodies, made of a periodic and specifically designed three-dimensional assembly of beams. Derivation is performed in the framework of the direct 1D approach, while the constitutive law is determined by a homogenization procedure based on an energy equivalence between a cell of the periodic model and a segment of the solid beam. Warping of the cross-section, caused by shear and torsion, is approximatively taken into account by the concept of a shear factor, namely, a corrective factor for the constitutive coefficients of the equivalent beam. The inertial properties of the Timoshenko model are analytically identified under the hypothesis, and the masses are lumped at the joints. Linear static and dynamic responses of some micro-structured beams, taken as case studies, are analyzed, and a comparison between the results given by the Timoshenko model and those obtained by Finite-Element analyses on 3D frames is made. In this framework, the effectiveness of the equivalent model and its limits of applicability are highlighted.

scholarly journals Investigation of the Torsional Effects on the Lateral Buckling of a Pipe-Like Beam Resting on the Ground under Axial Compression

2020 ◽  
Vol 20 (09) ◽  
pp. 2050110
Author(s):  
Philippe Le Grognec ◽  
Alain Nême ◽  
Jie Cai
Keyword(s):  
Critical Loads ◽  
Neutral Axis ◽  
Constitutive Law ◽  
Classical Solutions ◽  
Beam Model ◽  
Bottom Line ◽  
Lateral Buckling ◽  
Offshore Pipelines ◽  
Buckling Modes ◽  
Buckling Behavior

This paper deals with the lateral buckling behavior of an axially compressed beam interacting with the ground on which it is resting. Such a simple model is supposed to reproduce the same trends as observed during the lateral buckling of offshore pipelines on the seabed. In such practical analyses, the pipe-soil interaction relates the ground to the neutral axis of the pipeline. It is shown that, although such a constraint significantly affects the buckling behavior of the pipeline, it cannot reflect the torsional component of the buckling modes. However, this component is encountered in practice and may further modify the critical loads. Therefore, in this present preliminary study, the interaction between the beam in hand and the surrounding ground is modeled by a connection (a continuous distribution of lateral springs) related to the bottom line of the beam. In this way, the real contact between the soil and the bottom line of a pipe is mimicked, allowing for both flexural and torsional deformations in the buckling response. The problem is investigated analytically using an Euler–Bernoulli beam model with an isotropic linear elastic constitutive law and also an elastic interaction law. Original analytical solutions are derived and compared to numerical results obtained through finite element computations. In comparison with classical solutions (with the connection related to the neutral axis), new types of buckling modes may appear when considering torsional effects, depending on the boundary conditions, with generally much lower critical loads. These first results are certainly representative of some features of the global/localized lateral buckling of offshore pipelines, indicating that torsional effects should also be taken into account in such more comprehensive analyses.

scholarly journals Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

2021 ◽  
Vol 11 (21) ◽  
pp. 10434
Author(s):  
Faraz Kiarasi ◽  
Masoud Babaei ◽  
Kamran Asemi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Three Dimensional ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Combined Loading ◽  
Rectangular Plates ◽  
Loading Conditions ◽  
Classical Elasticity ◽  
Novel Approach ◽  
Buckling Behavior ◽  
Generalized Differential

The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed systematically to study the sensitivity of the buckling response of porous structures, to different input parameters, such as the aspect ratio, porosity and Skempton coefficients, along with different boundary conditions (BCs) and porosity distributions, with promising and useful conclusions for design purposes of many engineering structural porous members.

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.

Evaluation of a Strain Energy Equivalence Principle (SEEP)-Based Continuum Damage Model

2007 ◽  
Vol 353-358 ◽  
pp. 1199-1202
Author(s):  
Usik Lee ◽  
Deokki Youn ◽  
Sang Kwon Lee
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Damage Model ◽  
Elastic Stiffness ◽  
Constitutive Law ◽  
Mode Shapes ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Square Plate

A new continuum damage theory (CDT) has been proposed by Lee et al. (1997) based on the SEEP. The CDT has the apparent advantage over the other related theories because the complete constitutive law can be readily derived by simply replacing the virgin elastic stiffness with the effective orthotropic elastic stiffness obtained by using the proposed continuum damage theory. In this paper, the CDT is evaluated by comparing the mode shapes and natural frequencies of a square plate containing a small line-through crack with those of the same plate with a damaged site replaced with the effective orthotropic elastic stiffness computed by using the CDT.

An Analytical Shape Memory Polymer Composite Beam Model for Space Applications

2016 ◽  
Vol 16 (02) ◽  
pp. 1450093 ◽  
Author(s):  
D. Bergman ◽  
B. Yang
Keyword(s):  
Shape Memory ◽  
Polymer Composite ◽  
Geometric Model ◽  
Shape Memory Polymer ◽  
Constitutive Law ◽  
Finite Difference Approximation ◽  
Dynamic Equations ◽  
Difference Approximation ◽  
Beam Model ◽  
Space Applications

Shape memory polymer composite (SMPC) structures, due to their ability to be formed into a small compact volume and then transform back to their original shape, are considered as a solution in the design of light-weight large deployable space structures. There is a wide array of constitutive and qualitative work being done on SMPC’s but little or no development of dynamic equations. This paper documents a macroscopic model for the shape fixation and shape recovery processes of a SMPC cantilever beam. In particular the focus is on the shape fixation process, whereby a quasi-static equilibrium model can be used instead of a full equation of motion. Numerical results are obtained in this regard by use of finite difference approximation with Newton’s method. This formulation combines a nonlinear geometric model with a temperature dependent constitutive law. Additionally, the dynamic equations of the SMPC cantilever are derived. Future work will include a dynamic numerical model, and a finite element model of the SMPC structure.

2D Vector Cellular Automata Model for Simulating Fracture of Rock under Tensile Condition

2004 ◽  
Vol 261-263 ◽  
pp. 705-710 ◽  
Author(s):  
Ming Tian Li ◽  
Xia Ting Feng ◽  
Hui Zhou
Keyword(s):  
Cellular Automata ◽  
Fracture Process ◽  
Constitutive Law ◽  
Cellular Automata Model ◽  
Complex Fracture ◽  
Intrinsic Parallelism ◽  
A Cell ◽  
Direct Tensile ◽  
In Virtue Of ◽  
Simple Fracture

Based on the cellular automata of the plane truss structure, a 2D cellular automata model is presented to simulate the fracture of rock at meso-level. Cellular automata are made up of cell, states, lattice, neighbor and rule. Rock is divided into lattice in which each lattice point presents a cell. Each cell is assumed to connect with several cells, which are called as its neighbors, in virtue of truss elements. The truss elements can adopt some different simple local laws, i.e. constitutive law, which may be elastic or elastic-plastic and the simple fracture rule. It also can adopt different mechanical properties, which present their heterogeneity and anisotropy. This model can make full use of the advantages of cellular automata such as its intrinsic parallelism, localization and so on. In the meantime, as a powerful tool to analyze the nonlinear, complex system, cellular automata can be used to study the nonlinear, complex fracture process. The model is used to simulate the direct tensile of the rock plates, the complete fracture process and the stress-strain curves are attained which are accordance with the experiment.

scholarly journals Contributions of Strain Energy and PV-work on the Bending Behavior of Uncoated Plain-woven Fabric Air Beams

2007 ◽  
Vol 2 (1) ◽  
pp. 155892500700200 ◽  
Author(s):  
Paul V. Cavallaro ◽  
Ali M. Sadegh ◽  
Claudia J. Quigley
Keyword(s):  
Strain Energy ◽  
Constitutive Relations ◽  
Mechanical Tests ◽  
Woven Fabric ◽  
Beam Model ◽  
Bending Performance ◽  
Macro Scale ◽  
Beam Bending ◽  
Bending Behavior ◽  
Homogenization Methods

The bending performance of fabric air beams varies significantly from conventional beams. Both are dependent upon the constitutive relations of the material, but air beams are further dependent upon the thermodynamics of the internal air. As the governing energy balance demonstrates, air beam bending is dependent upon strain energy and PV-work (air compressibility). The relative importance of these terms will vary with pressure, volume changes and shear deformations. To this point, a swatch of uncoated plain-woven fabric was subjected to mechanical tests and its material properties determined. Attempts at using the stress-strain measurements in air beam models, assumed constructed with the same fabric, were made. The models accounted for fluid-structure interactions between the air and fabric. Homogenization methods were used and were necessary to provide computational efficiencies for the macro-scale air beam model while attempts were made to incorporate the combined extension and shear behaviors observed during the material tests. Bending behavior was numerically investigated for several constitutive cases. The models were solved with the ABAQUS-Explicit program over a range of pressures. The fabric strain energy and PV-work were tracked and compared. It was concluded that strain energy and PV-work must be considered in deflection analyses of uncoated plain-woven fabric air beams.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

2020 ◽  
pp. 095440622092068
Author(s):  
Marina Trajković-Milenković ◽  
Otto T Bruhns ◽  
Andrija Zorić
Keyword(s):  
Plastic Material ◽  
Constitutive Relations ◽  
Relevant Literature ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Elastoplastic Deformations ◽  
Perfectly Plastic ◽  
User Subroutine ◽  
Shear Problem ◽  
Elastic Perfectly Plastic

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

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