Finite Element Formulation For Analysis Research Articles

Mixture Theory-Based Finite Element Approach for Analyzing the Edematous Condition of Biological Soft Tissues.

In hydrated soft biological tissues experiencing edema, which is typically associated with various disorders, excessive fluid accumulates and is encapsulated by impermeable membranes. In certain cases of edema, an indentation induced by pressure persists even after the load is removed. The depth and duration of this indentation are used to assess the treatment response. This study presents a mixture theory-based approach to analyzing the edematous condition. The finite element analysis formulation was grounded in mixture theory, with the solid displacement, pore water pressure, and fluid relative velocity as the unknown variables. To ensure tangential fluid flow at the surface of tissues with complex shapes, we transformed the coordinates of the fluid velocity vector at each time step and node, allowing for the incorporation of the transmembrane component of fluid flow as a Dirichlet boundary condition. Using this proposed method, we successfully replicated the distinct behavior of pitting edema, which is characterized by a prolonged recovery time from indentation. Consequently, the proposed method offers valuable insights into the finite element analysis of the edematous condition in biological tissues.

Buckling and vibration analysis of axially functionally graded nanobeam based on local stress- and strain-driven two-phase local/nonlocal integral models

This paper presented an efficient finite element formulation for analysis of the buckling and free vibration of the axial functionally graded (AFG) Euler-Bernoulli nanobeam based on minimum total potential energy principle with linear constraints. The stress- and strain-driven two-phase local/nonlocal integral models are utilized to address small scale effects. The material properties of the AFG nanobeam vary exponentially along the axial direction. The nonlocal integral constitutive equation can be equivalently transformed into a differential equation with two constitutive boundary conditions. The governing equation and standard boundary conditions are derived via Hamilton's principle. The weak form associated with total potential energy is derived and the constitutive boundary conditions can be converted to external forces at the boundaries. By employing a numerical solution methodology on the basis of the finite element method (FEM) together with Lagrangian multiplier method (LMM), a unified finite element formulation based on stress- and strain-driven two-phase local/nonlocal elasticity is constructed to obtain the critical buckling load and vibration frequency. Meanwhile, the numerical results obtained through generalized differential quadrature method (GDQM) validate the efficiency and accuracy of the present results. The influence of gradient index, nonlocal parameter and local phase parameter on buckling and free vibration of AFG Euler-Bernoulli nanobeam is investigated in detail under different nonlocal models and boundary conditions. It is demonstrated that the gradient index has more effect on mode shapes than the buckling load and vibration frequency between the local stress- and strain-driven two-phase local/nonlocal models.

Vibration analysis of composite plates reinforced CNTs using an exponential function approach

Free vibration analysis of functionally graded material ‘FGM’ plates reinforced with carbon nanotubes (CNTs) using exponential distribution law is investigated. Nonlinear distribution through the thickness direction of Nano-fillers is considered in the present study. Thus, the mechanical properties of the nanotubes vary through the thickness and are evaluated using a modified rule of mixture. In the finite element analysis formulation, the first-order shear deformation theory has been implemented by using the exponential law. The obtained results show a better distribution of CNTs through the thickness, which leads to an improved plate stiffness. An increase in the natural frequencies is thus expected. The obtained results show the five natural frequencies which compare well with those available in the literature.

Large displacement analysis of laminated beam-type structures

The paper presents a finite element formulation for analysis of 3D framed structures with thin-walled laminated composite cross-sections, using a co-rotational approach. The formulation considers the effects of large displacements on the response of space frames subjected to conservative and static external loads. Classical lamination theory for thin fiber-reinforced laminates has been employed. Stability analysis is performed in load deflection manner using co-rotational formulation. The shear strain of the middle surface is assumed to be zero, and the cross-section is not distorted in its own plane. In order to illustrate the application of the proposed formulation, several numerical examples are presented.

A novel hybrid isogeometric element based on two-field Hellinger–Reissner principle to alleviate different types of locking

In the present work, novel hybrid elements are proposed to alleviate the locking anomaly in non-uniform rational B-spline-based isogeometric analysis (IGA) using a two-field Hellinger–Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress fields. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains that are severely affected by volumetric locking along with the thin plate and shell problems where the shear locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation is not restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against both shear and volumetric locking.

A geometrically nonlinear variable-kinematics continuum shell element for the analyses of laminated composites

To facilitate further gains in structural efficiency, the use of composite materials in engineering structures is on the rise. Simultaneously, a drive for thinner components is leading to structural behaviour that is governed by elastic nonlinearities such as large deflections and instabilities. For efficient and reliable design, numerical models must predict the nonlinear displacements, as well as the corresponding stress and strain responses, both accurately and at minimal computational cost. In this work, we present a novel tensor-based variable kinematics continuum shell (VKCS) formulation that is geometrically nonlinear in a total Lagrangian sense. The key contribution is the development and validation of a nonlinear continuum shell model that is completely general in terms of its geometric and kinematic descriptions. The governing equations are derived and presented in tensorial form, which enables a straightforward spatial mapping for models with complex curvatures. The ‘variable-kinematics’ capability means that the element field variables can be refined in a hierarchical and orthotropic manner, i.e. the in-plane and through-thickness displacements can be independently discretised using any polynomial functions with arbitrary orders of expansion. With this feature, the model configurations can be tailored for specific nonlinear problems, whilst also achieving fast solution convergence rate through the use of higher-order basis functions. For validation, the VKCS model has been benchmarked against existing nonlinear problems in the literature that feature large displacements with complex equilibrium paths. In addition, we have proposed two new benchmarks to investigate the 3D Cauchy stress in a snapped shallow roof, and the postbuckling behaviour of a wind turbine blade section. The VKCS formulation is shown to be a versatile tool that allows the user to easily switch between a multitude of model configurations, and can thus accommodate the varying fidelity of analyses required across different design stages. Furthermore, our benchmarks have demonstrated that the variable-kinematics model requires fewer degrees of freedom and run time to track complex 3D stresses when compared to conventional low-order continuum elements. • A novel hierarchical finite element formulation for analysis of laminated structures. • Easily switch between model configurations required across different design stages. • Shell element with completely general geometric and kinematic discretisation. • 3D stress tracking in snapped roof and post-buckling analysis of wind turbine blades.

A novel stress-based formulation of finite element analysis

A novel stress-based formulation of finite element analysis

A Thermal–Elastic–Plastic Constitutive Model using the Radial Basis Function Neural Network and Application for an Energy Efficient Warm Forming Process

This work presents a thermal–elastic–plastic constitutive equation based on the radial basis function (RBF) artificial neural network and application with the finite element (FE) analysis. In order to capture the stress data in the coupled temperature-strain doamin, a constitutive equation was defined based on the RBF model, and the trained model was validated by test data that were not used in the training. The RBF based constitutive model was then combined with the stress integration and tangent modulus formulation of FE analysis to apply the new model to a warm V-bending process that includes elastic–plastic deformation and elastic recovery under non-isothermal conditions. The heating method was the infrared (IR) local heating method. The results show that the RBF constitutive model can provide good agreement with the experimental data for V-bending in the non-isothermal conditions. The effects of the parameters of the basis function are also discussed in this work.

Computational Modeling of Dislocation Slip Mechanisms in Crystal Plasticity: A Short Review

The bridge between classical continuum plasticity and crystal plasticity is becoming narrower with continuously improved computational power and with engineers’ desire to obtain more information and better accuracy from their simulations, incorporating at the same time more effects about the microstructure of the material. This paper presents a short overview of the main current techniques employed in crystal plasticity formulations for finite element analysis, as to serve as a point of departure for researchers willing to incorporate microstructure effects in elastoplastic simulations. We include both classical and novel crystal plasticity formulations, as well as the different approaches to model dislocations in crystals.

Nonlinear Finite Element Analysis Formulation for Shear in Reinforced Concrete Beams

This study suggests a novel beam-column element formulation that utilizes an equilibrium-driven shear stress function. The beam shear is obtained from the bi-axial states of micro-planes, through matrix condensation and zero vertical traction assumptions. This properly remedies the shear stiffening of a one-dimensional beam-column element, keeping its degrees of freedom to a minimum. For verification of the proposed method, a total of seven shear test results of reinforced concrete (RC) beams were collected from the literature, in which the key variables were the reinforcement ratio, the presence of shear reinforcement, and section shape. The advantages are clearly shown in the shear stresses distributions being accurately described and the global load-displacement relations being successfully obtained and matching well with various test results. The proposed model shows satisfactory descriptions of the monotonic load-displacement response of the RC beams failing in multiple modes that vary from diagonal-tension to flexural-compression. In addition, more accurate and reliable information of sectional responses including sectional shear deformation and stresses is collected, leading to better prediction of a potential shear failure mode. Finally, the advantages of the proposed model are demonstrated by comparing the analysis results of an RCT-beam by using the different shear assumptions that include the constant and parabolic shear strains, constant shear flow, and the proposed shear stress function.

High-order triangular finite elements applied to visco-hyperelastic materials under plane stress

A finite element formulation for analysis of highly deformable viscoelastic materials under plane stresses is presented. The element is the isoparametric plane triangle of any-order. The constitutive modeling is based on a Lagrangian visco-hyperelastic framework, in which the multiplicative split of the deformation gradient is used. The internal variable employed is the viscous right Cauchy–Green stretch tensor. The work is restricted to the compressible neo-Hookean hyperelastic law, the Zener rheological model and an isochoric nonlinear evolution equation, although other models can be further implemented. The plane stress condensation and the compact 2D constitutive relation are described. Three large deformation problems are numerically analyzed to validate the methodology: a membrane with high compressive strain levels and mesh distortion; a perforated plate with stress concentration; and a circular ring under nonlinear bending. Meshes with different element orders (from linear to sixth) are employed. Results confirm that, except for the linear degree, mesh refinement completely remove locking problems, providing an accurate and, thus, a reliable prediction of the mechanical behavior. It is also demonstrated that the creep phenomenon can be reproduced in finite strain regime. The novelty of the paper is the convergence analysis regarding displacements, strains and stresses in the context of plane stress visco-hyperelasticity.

Recommended Finite Element Formulations for the Analysis of Offshore Blast Walls in an Explosion

Abstract This study suggests relevant finite element (FE) formulations for the structural analysis of offshore blast walls subjected to blast loadings due to hydrocarbon explosions. The present blast wall model adopted from HSE (2003) consists of a corrugated panel and supporting members, and was modelled with shell, thick-shell, and solid element combinations in LS-DYNA, an explicit finite element analysis (FEA) solver. Stainless and mild steels were employed as materials for the blast wall model, with consideration of strain rate effect throughout ten (10) pulse pressure load regimes. The obtained FEA results were validated by experimental data from HSE (2003) with decent agreement. In the present study, recommended FE formulations with additional hourglass control functions were widely discussed from the perspectives of solution accuracy and computational cost based on a statistical approach. The obtained outcomes could be used for the structural analysis and design of offshore blast walls in the estimations of maximum and permanent deformations under blast loadings.

A mixed 3D-1D finite element formulation for analysis of geomaterial structures with embedded curvilinear inclusions: application to load transfer in mooring anchor systems

Abstract A finite element model for structural analysis of media with embedded inclusions is presented. The “embedded element concept” is adopted to model the contact interaction of two medium components along the contact interface considering a mixed 3D-1D formulation. The Mohr-Coulomb interface model is employed to define the bond-stress and bond-slip relation and strains associated with bond-slip are assumed to remain infinitesimal along the interface. Nonlinear analysis is performed with a corotational kinematics description introduced in the context of embedded approach. The problem of load transfer in mooring anchor systems was investigated and reasonable results were obtained using the present model.

Stabilized Low-Order Explicit Finite Element Formulations for the Coupled Hydro-Mechanical Analysis of Saturated Poroelastic Media

We developed new stabilized low-order explicit finite element formulations for analysing the fully coupled hydro-mechanical behaviour of fluid-saturated poroelastic media. For space stabilization, the low-order U-p finite element employs two stabilization schemes. One stabilization scheme is based on the polynomial pressure projection technique in the fluid phase. The other one assumes enhanced strain field for the solid-phase terms. For time stabilization, an unconditionally stable explicit integration formula is proposed for discretization in the time domain to eliminate the time-step-size sensitivity of the temporal discretization finite difference format. The performance of the proposed formulations is demonstrated through four numerical examples. The proposed formulations not only agree strongly with the analytical/reference solutions, but also yield unconditionally stable high-precision results that outperform the standard finite element combined finite difference scheme. The modelling results indicate the proposed schemes possess significant advantages in terms of precision and computational efficiency for large timescales and adaptability to space-domain discretization. The proposed schemes have great potential in engineering applications for large timescale problems.

Nonparametric Online Learning Control for Soft Continuum Robot: An Enabling Technique for Effective Endoscopic Navigation.

Bioinspired robotic structures comprising soft actuation units have attracted increasing research interest. Taking advantage of its inherent compliance, soft robots can assure safe interaction with external environments, provided that precise and effective manipulation could be achieved. Endoscopy is a typical application. However, previous model-based control approaches often require simplified geometric assumptions on the soft manipulator, but which could be very inaccurate in the presence of unmodeled external interaction forces. In this study, we propose a generic control framework based on nonparametric and online, as well as local, training to learn the inverse model directly, without prior knowledge of the robot's structural parameters. Detailed experimental evaluation was conducted on a soft robot prototype with control redundancy, performing trajectory tracking in dynamically constrained environments. Advanced element formulation of finite element analysis is employed to initialize the control policy, hence eliminating the need for random exploration in the robot's workspace. The proposed control framework enabled a soft fluid-driven continuum robot to follow a 3D trajectory precisely, even under dynamic external disturbance. Such enhanced control accuracy and adaptability would facilitate effective endoscopic navigation in complex and changing environments.

Long-term fatigue behavior of a cantilever piezoelectric energy harvester

Piezoelectric energy harvesting has attracted extensive research in the advancement of new designs and techniques over the last decade. The cantilever shaped piezoelectric energy harvesting beam is one of the most employed designs, due to its simplicity and flexibility for further performance enhancement. The strain distribution along the cantilever piezoelectric energy harvesting beam is nonuniform, which would induce fatigue damage at the root of the cantilever on the long run. This particular issue has seldom been addressed in the literature. This article presents an experimental investigation on the fatigue behavior of a cantilever piezoelectric energy harvesting beam at different base excitation levels. The experimental study is augmented with analytical formulation to examine the strain levels and with finite element analysis formulation to model the piezoelectric energy harvesting beam with a macro fiber composite piezoelectric transducer. A two-dimensional model is developed based on the three-dimensional model to investigate crack propagation in the piezoelectric energy harvesting beam. Furthermore, the electromechanical impedance technique is employed to monitor the progression of damage in the experimental specimens. The root mean square deviation and relative root mean square deviation of the impedance values and voltage obtained from the macro fiber composite transducer provide a profound introspection into the damage propagation in the piezoelectric energy harvesting beam. This study provides an insight into the behavior of the piezoelectric energy harvesting beam undergoing fatigue loading due to a uniform sinusoidal base excitation by analyzing the output voltage, resonant frequency, tip displacement, tip velocity, and impedance variations. It will pave the way for future studies on the fatigue-based design guides for piezoelectric energy harvesting beams.

Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

We present a geometrically nonlinear finite element formulation for analysis of functionally graded 3D beams. The proposed formulation employs the continuum mechanics based beam element with the warping displacement to model complex modes of deformation. The novelty of the developed method is that the warping function can be accurately calculated for any beam with arbitrary cross-sections and material grading patterns. Superb performances of the proposed beam element are demonstrated through several representative examples.

Contamination of roadside soils by runoff pollutants: A numerical study

Roadway runoff contains multiple pollutant species that can contaminate roadside water, pose risks to aquatic organisms, and cause health problems for human beings. Roadside soils, mostly in their unsaturated states, constitute the first receiving entity for runoff water as the water flows off roadway surfaces. Considering the time-consuming and sophisticated procedures required for experimentally characterizing the soil–water characteristics of unsaturated soils, a finite element analysis (FEA) model was developed in this study and used to predict the contaminating process of variably saturated soils by the pollutants carried in runoff. The governing equation for the transport of multiple pollutant species was formulated based on the mass transport equation for porous media and the Richards’ Equation for characterizing variably saturated soils. FEA formulation of the governing equation was accomplished by implementing a linear interpretation function in three-node triangular elements. The FEA model was validated using a miniature laboratory model. The validated FEA model was then implemented to analyze the contamination of a roadside ditch by studying different configurations of soil stratum. The FEA model developed in this work allows the prediction of pollutant distributions in soils at any time of interest, which will greatly facilitate the management of contamination problems caused by roadway runoff.

Isogeometric bending analysis of composite plates based on a higher-order shear deformation theory

This research paper presents an isogeometric plate finite element formulation for analysis of thick composite plates. Isogeometric finite element method which is based on non-uniform rational B-splines (NURBS) basis functions, is a novel numerical procedure developed to bridge the gap between CAD and FEM modeling of structures. In order to investigate the behavior of isogeometric plate elements under static loading, plate kinematics is based on third order shear deformation theory (TSDT) of Reddy, which is free from transverse shear locking. This paper discusses accurate transverse stress recovery procedures for TSDT isogeometric finite elements. Numerical experiments with quadratic, cubic and quartic elements are presented and obtained results are compared to other available ones.

Beam–solid contact formulation for finite element analysis of pile–soil interaction with arbitrary discretization

SUMMARYThis paper presents an embedded beam formulation for discretization independent finite element (FE) analyses of interactions between pile foundations or rock anchors and the surrounding soil in geotechnical and tunneling engineering. Piles are represented by means of finite beam elements embedded within FEs for the soil represented by 3D solid elements. The proposed formulation allows consideration of piles and pile groups with arbitrary orientation independently from the FE discretization of the surrounding soil. The interface behavior between piles and the surrounding soil is represented numerically by means of a contact formulation considering skin friction as well as pile tip resistance. The pile–soil interaction along the pile skin is considered by means of a 3D frictional point‐to‐point contact formulation using the integration points of the beam elements and reference points arbitrarily located within the solid elements as control points. The ability of the proposed embedded pile model to represent groups of piles objected to combined axial and shear loading and their interactions with the surrounding soil is demonstrated by selected benchmark examples. The pile model is applied to the numerical simulation of shield driven tunnel construction in the vicinity of an existing building resting upon pile foundation to demonstrate the performance of the proposed model in complex simulation environments. Copyright © 2014 John Wiley & Sons, Ltd.