A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Higher-order assumed strain plane element immune to mesh distortion

2020 ◽  
Vol 37 (9) ◽  
pp. 2957-2981 ◽  
Author(s):  
Mohammad Rezaiee-Pajand ◽  
Nima Gharaei-Moghaddam ◽  
Mohammadreza Ramezani
Keyword(s):  
Degrees Of Freedom ◽  
Triangular Element ◽  
Mesh Distortion ◽  
Content Type ◽  
Assumed Strain ◽  
Plane Element ◽  
Displacement Based ◽  
Locking Phenomena ◽  
Assumed Strain Method ◽  
Better Than

Purpose This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

On the selection of the most plausible non-linear axial stress–strain model for railway ballast under different impulse magnitudes

2021 ◽  
pp. 147592172110339
Author(s):  
Mujib Olamide Adeagbo ◽  
Heung-Fai Lam ◽  
Qin Hu
Keyword(s):  
Small Amplitude ◽  
Model Updating ◽  
Axial Stress ◽  
Elastic Model ◽  
Stress Strain ◽  
Elasticity Limit ◽  
Non Linear ◽  
Model Class ◽  
Strain Model ◽  
Selection Of

The effective maintenance and health monitoring of ballasted railway tracks, which involves the determination of differential settlement, track support stress and stiffness, and the strain-hardening property of ballast, is essential. The vertical stress–strain behavior of the ballast layer is primarily responsible for the irrecoverable strains and settlements in tracks, leading to further track degradation. This article reports the development of a series of applicable yet simple uniaxial models and the selection of the most plausible one for capturing the behavior of vertical stresses and strains in ballasts utilizing a set of measured vibration data of the rail–sleeper–ballast system from a Bayesian perspective. From the literature, the dynamic behavior of ballast can be divided into linear and non-linear regions. Under small amplitude vibration, the stress–strain property is linear and elastic, while the behavior becomes non-linear and inelastic once the elasticity limit is exceeded. By integrating the linear phase to some well-known non-linear engineering material laws, a list of new ballast stress–strain model classes was developed. An enhanced Markov chain Monte Carlo–based Bayesian scheme was utilized to explicitly handle the uncertainties in the model updating process, while the Bayesian model class selection method was employed to select the most plausible ballast stress–strain model class under the prevailing system conditions. The proposed methodology was verified using three sets of measured acceleration data from impact hammer tests on an in situ sleeper with simulated ballast damage. The obtained results suggest that the linear-elastic model is sufficient for small amplitude vibrations, while the modified Voce model is the most plausible amongst the investigated model classes for high impact load. The results also demonstrate the importance of the non-linear ballast model in ballast damage identification and the potential applicability of the selected ballast model in field track monitoring.

scholarly journals Bias Truck Tire Deformation Analysis with Finite Element Modeling

2020 ◽  
Vol 10 (12) ◽  
pp. 4326
Author(s):  
Józef Pelc
Keyword(s):  
Incompressible Material ◽  
Axisymmetric Deformation ◽  
Thermal Shrinkage ◽  
Deformation Analysis ◽  
Truck Tire ◽  
Non Linear ◽  
Strain Relationship ◽  
Tire Modeling ◽  
Total Lagrangian Formulation

This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.

scholarly journals An Improved Lagrangian-Inverse Method for Evaluating the Dynamic Constitutive Parameters of Concrete

Materials ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1871
Author(s):  
Xinlu Yu ◽  
Yingqian Fu ◽  
Xinlong Dong ◽  
Fenghua Zhou ◽  
Jianguo Ning
Keyword(s):  
High Speed ◽  
Inverse Method ◽  
Image Correlation ◽  
Analysis Method ◽  
Stress Strain ◽  
Optical Techniques ◽  
Element Simulation ◽  
Non Linear ◽  
Constitutive Parameters ◽  
Inverse Analysis Method

The dynamic constitutive behaviors of concrete-like materials are of vital importance for structure designing under impact loading conditions. This study proposes a new method to evaluate the constitutive behaviors of ordinary concrete at high strain rates. The proposed method combines the Lagrangian-inverse analysis method with optical techniques (ultra-high-speed camera and digital image correlation techniques). The proposed method is validated against finite-element simulation. Spalling tests were conducted on concretes where optical techniques were employed to obtain the high-frequency spatial and temporal displacement data. We then obtained stress–strain curves of concrete by applying the proposed method on the results of spalling tests. The results show non-linear constitutive behaviors in these stress–strain curves. These non-linear constitutive behaviors can be possibly explained by local heterogeneity of concrete. The proposed method provides an alternative mean to access the dynamic constitutive behaviors which can help future structure designing of concrete-like materials.

scholarly journals Non-linear elastic model incorporating temperature effects

2018 ◽  
Vol 5 (1) ◽  
pp. 22-30 ◽  
Author(s):  
Hong Liu ◽  
Hanlong Liu ◽  
Yang Xiao ◽  
Qingsheng Chen ◽  
Yufeng Gao ◽  
...  
Keyword(s):  
Temperature Effects ◽  
Elastic Model ◽  
Linear Elastic ◽  
Linear Elastic Model ◽  
Non Linear

An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2011 ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Element Analysis ◽  
Motion Direction ◽  
Form Analysis ◽  
Flexure Mechanism ◽  
Non Linear ◽  
Decoupled Motion ◽  
Motion Range ◽  
Parallel Kinematic ◽  
Cross Axis

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.

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