Solid Finite Element Research Articles

Stress-strain state of shell of revolution analysis by using various formulations of three-dimensional finite elements

The aim of the work is to perform a comparative analysis of the results of analyzing arbitrarily loaded shells of revolution using finite element method in various formulations, namely, in the formulation of the displacement method and in the mixed formulation. Methods. To obtain the stiffness matrix of a finite element a functional based on the equality of the actual work of external and internal forces was applied. To obtain the deformation matrix in the mixed formulation the functional obtained from the previous one by replacing the actual work of internal forces in it with the difference of the total and additional work was used. Results. In the formulation of the displacement method for an eight-node hexahedral solid finite element, displacements and their first derivatives are taken as the nodal unknowns. Approximation of the displacements of the inner point of the finite element was carried out through the nodal unknowns on the basis of the Hermite polynomials of the third degree. For a finite element in the mixed formulation, displacements and stresses were taken as nodal unknowns. Approximation of the target finite element values through their nodal values in the mixed formulation was carried out on the basis of trilinear functions. It is shown on a test example that a finite element in the mixed formulation improves the accuracy of the strength parameters of the shell of revolution stress-strain state.

Towards improving finite element solutions automatically with enriched 2D solid elements

In this paper, we propose an automatic procedure to improve the accuracy of finite element solutions using enriched 2D solid finite elements (4-node quadrilateral and 3-node triangular elements). The enriched elements can improve solution accuracy without mesh refinement by adding cover functions to the displacement interpolation of the standard elements. The enrichment scheme is more effective when used adaptively for areas with insufficient accuracy rather than the entire model. For given meshes, an error for each node is estimated, and then proper degrees of cover functions are applied to the selected nodes. A new error estimation method and cover function selection scheme are devised for the proposed adaptive enrichment scheme. Herein, we demonstrate the proposed enrichment scheme through several 2D problems.

A Three-Layer Quasi-3D Finite Element Analysis for Smart Actuation on Sandwich Plates

The quasi-3D finite element model includes the smart actuation on a three-layer sandwich plate with laminated composite face-sheets. In the model, the face-sheets are represented as Reissner-Mindlin plates and the core is modeled as a three-dimensional continuum. This representation allows accurate modeling for a wide range of core types. In this model, the electrical constitutive relations of piezoelectric layers are included in the formulation of the face-sheets. In previous publications, this quasi-3D finite element formulation has demonstrated some advantages in comparison with solid finite element models. The aspect ratio of three-dimensional elements can make it rather inconvenient to use on very thin faces-sheets, which makes the number of degrees of freedom very high. Analytical through-thickness integration of the energy expressions is used to reduce the three-dimensional problem to two dimensions for the evaluation of mass and stiffness matrices. In the same way, the analytical integration of the electrical voltages work applied to the piezoelectric layers produces the piezoelectric actuation force vector. This research assesses the accuracy of the proposed model for dynamic responses of sandwich plates using a broad range of core-to-face-sheet stiffness ratio. The numerical results show that deflections promoted by the voltage applied to piezoelectric layers of the sandwich plate are very small, even if the core is very flexible. The results also indicate that the core flexibility strongly affects the natural frequencies of the higher bending modes.

An Improved Approach to Direct Simulation of an Actual Almen Shot Peening Intensity Test with a Large Number of Shots.

In existing simulations of the Almen intensity test, arc height is indirectly obtained by an equivalent method including a representative cell, a few shots and equivalent loading. Most of these equivalent methods cannot consider the transverse deformation of the strip, the complex stress state of the plastic hardening layer and process parameters, resulting in deviation from the actual test. This paper introduces an improved and experimentally validated discrete element model (DEM)-finite element model (FEM) to predict the actual Almen intensity. The improvement of this model is mainly reflected in the large and real number of shots involved in the actual Almen intensity test, shot–shot interactions, and real-size solid finite element model of the Almen strip. A new method for calculating the shot stream is proposed based on the test and considering test process parameters such as the mass flowrate, nozzle movement speed and nozzle–workpiece distance. The shot stream impacting the strip with a fully restrained underside was first simulated in improved DEM-FEM to bring the forming energy. As a second step, an implicit solver of the Almen strip FEM calculates the spring-back to simulate strip removal from the holder. The results achieved by the present approach are compared with the results obtained by the experimental results and those in the literature. The results show that the arc height and Almen intensity obtained by the present approach match much better with the literature than the traditional method. Some new results obtained by the improved coupling DEM-FEM method are presented. The influences of the transverse deformation and surface plastic layer on the deformation of the Almen strip are discussed. This improved method provides an alternative characterization method for precision peen forming simulation.

A concurrent multiscale approach for modeling recycled aggregate concrete

The use of recycled concrete aggregates in new concrete is an alternative that can provide economical and environmental benefits. However, the influence of the inert particles on the mechanical behavior of concrete needs to be better understood. To provide a comprehensive simulator to predict the failure mechanism of this material taking into account its heterogeneity in mesoscale, a mesh fragmentation technique composed of interface solid finite elements equipped with a tensile damage model is employed. To minimize computational costs, a concurrent multiscale strategy based on the use of coupling finite elements to connect the macro and mesoscale regions is adopted. In mesoscale, the different phases of the recycled aggregate concrete (RAC) are explicitly represented, consisting of: (i) new mortar matrix; (ii) recycled aggregate composed of old matrix and crushed rock (natural aggregate); and (iii) interfacial transition zones in between all of them. For the regions where cracks are not expected, homogenized elastic parameters are assumed for the RAC. Three-point bending beams experimentally tested by Casuccio et al. [4] are numerically analyzed for concrete with compressive strength targets of 18, 37 and 48 MPa. These concrete beams were produced with coarse aggregates derived from natural crushed stone and another two coming from recycled concrete with high and normal strengths. The numerical results obtained show that the concurrent multiscale model is able to represent the tensile failure mechanism of the RAC, taking into account explicitly the effects of the recycled components on crack patterns and structural predictions.

A six-node prismatic solid finite element for geometric nonlinear problems in elasticity

The present work deals with an extended six-node prismatic 3D solid finite element to the analysis of nonlinear geometrical problems. The kinematic formulation is based on a virtual Space Fiber Rotation (SFR) concept which conducts to improve the displacement fields with additional displacement terms, presenting rotational degrees of freedom (DOFs). Once the standard and patch tests for linear validation are previously achieved, the present element is assessed again for large displacement and moderate rotation. For this purpose, the total Lagrangian approach is used and the Green–Lagrange strain/Piola–Kirchhoff​ stress tensors are considered. The material behavior considered in this work is restricted to Saint-Venant–Kirchhoff model for 3D large displacements elasticity To demonstrate the efficiency and accuracy of the developed finite element model, extensive and standard nonlinear benchmarks are presented. The obtained results show a good convergence and accuracy compared to similar finite elements and consequently well capability of the present element to deal with geometric nonlinear problems, including prediction of several limit points.

Progressive damage analysis and failure load of ceramic matrix composite hollow-shaft

Composite damage is one of important reasons for the destruction of engineering structures; therefore the research target is a typical engineering component – hollow shaft. Firstly, based on the continuum damage mechanics, a stiffness degradation method is proposed to simulate the progressive damage process of ceramic matrix composite hollow-shaft. Afterwards, program development using solid finite element method in ANSYS, the simulative load–displacement curves and tensile failure load of the hollow-shaft are achieved. Finally, Qualitative and quantitative analysis by computer calculation and experimental results, successfully predict the structure failure modes and bearing capacity under axial load. This work proves that the correctness and feasibility of this progressive damage analysis method for ceramic matrix composite hollow-shaft, and further deepen the understanding of damage development.

Computational and experimental investigation of progressive damage accumulation in I-plate composite structure

As the research object to the I-plate composite structure, a stiffness degradation method is developed by combined continuum damage mechanics with the solid finite element analysis method. The Tsai-Wu failure criterion is applied for structural damage initiation. Additionally, exponential equation associated with stress is used to simulate damage development. Based on the progressive damage model established, a 3D finite element technique is proposed to perform the progressive failure process in ANSYS. The structural damage development and simulated load–displacement curve are received, and compared with experimental results under transverse bending load. The compare results show the validity of progressive damage analysis method.

ОПРЕДЕЛЕНИЕ НАПРЯЖЁННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ КОРОТКИХ ВНЕЦЕНТРЕННО-СЖАТЫХ ТРУБОБЕТОННЫХ КОЛОНН МЕТОДОМ КОНЕЧНЫХ ЭЛЕМЕНТОВ ПУТЁМ СВЕДЕНИЯ ТРЁХМЕРНОЙ ЗАДАЧИ К ДВУМЕРНОЙ

The article presents the derivation of the FEM equations, which make possible to calculate short concrete-filled steel tubular columns in a plane elastic formulation. Steel tube is modeled by 1D bar finite elements. The obtained results are compared with the results of calculations using 3D solid and shell finite elements.

Three-Dimensional Solid Finite Element Contact Model for Rotordynamic Analysis: Experiment and Simulation

Abstract Conventional rotordynamic analyses generally treat the rotor as a continuous body without considering effect of clamped joints. However, in modern rotating machines, rotors are often assembled with multiple complex-shaped parts and joints, which may significantly affect rotordynamic behavior. Several authors have proposed methods for implementing contact effects in rotordynamic analysis, but a more general modeling method for handling arbitrary contact geometries with various levels of surface roughness is needed. The present paper suggests a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.

Development of a finite element via Unified Formulation: Implementation as a User Element subroutine to predict stress profiles in composite plates

Unified formulations (UF) have been increasingly used to analyze laminated plates and shells. A huge number of works was carried out via in-house software, but only few contributions were presented using UF linked to a FE commercial software. In addition, the implementation of a UF within a FE commercial software remains a black box. This work aims at unlocking the difficulties on implementing a UF within the FE software Abaqus. Therefore, an eight-node plate element is developed via a UF and implemented as a User Element subroutine (UEL). In order to evaluate potentialities and limitations of the implemented UEL subroutine, benchmarking cases are evaluated investigating laminated plates under concentrated and distributed load. The displacement fields and, mainly, stress profiles are predicated by three different approaches: i) in-house Matlab framework; ii) standard shell and solid finite elements from Abaqus; and iii) from self-developed finite elements using CUF (via UEL).

Research and Application of Cross Spatial Grid Method in Combined Box Girder Bridge with Corrugated Steel Webs

In order to further study the application of corrugated steel web composite box girder bridge in practical engineering, this paper selects a corrugated steel web box girder bridge with transverse diaphragms as the theoretical model, and uses the cross space grid method to simulate The model. Beam188 is the element type selected for this ANSYS modeling. The longitudinal element of the web is equivalent to a flat plate according to the plate and shell theory. The shape of the vertical element remains unchanged. Under the condition of its own weight, the natural frequency and deflection of the model are compared. The research results show that when the web is divided into whole and separated, the errors of the first-order natural frequencies of the two spatial mesh models and the solid finite element model are both within 10%, and the accuracy of the overall division is higher.

Analysis of temperature-induced deformation and stress distribution of long-span concrete truss combination arch bridge based on bridge health monitoring data and finite element simulation

Through decades of operation, deformation fluctuation becomes a central problem affecting the normal operating of concrete truss combination arch bridge. In order to clarify the mechanism of temperature-induced deformation and its impact on structural stress distribution, this article reports on the temperature distribution and its effect on the deformation of concrete truss combination arch bridge based on bridge health monitoring on a proto bridge with 138 m main span. The temperature distribution and deformation characteristics of the bridge structure in deep valley area are studied. Both of the daily and yearly temperature variation and structural deformation are studied based on bridge health monitoring. Using the outcome of monitoring data, three-dimensional solid finite element models are established to analyze the mechanism of temperature-induced deformation of the whole bridge under different temperature fields. The influence of temperature-induced effect is discussed on local damage based on the damage observation of the background bridge. The outcome of comparisons with field observation validates the analysis results. The relevant monitoring and simulation result can be referenced for the design and evaluation of similar bridges.

Influence of spatially varying material properties on the bimoment normal and shear stresses by warping torsion of FGM beams

In this contribution, which is an extension of author’s research [1,2], an influence of the in two and three directions varying material properties on non-uniform torsion of the Functionally Graded Material (FGM) thin-walled beams is originally investigated. Based on the semi-analytical solution of the fourth order differential equation for non-uniform torsion, the local finite element equations of the twisted FGM beam are presented, considering the non-uniform torsion with effect of warping and secondary deformations due to the angle of twist. The warping part of the first derivative of the twist angle caused by the bimoment is considered as an additional degree of freedom at the beam nodes. The Multi-Layers Method (MLM) [3], and the Reference Beam Method (RBM) [4] are extended for homogenization of the spatially varying material properties and relevant stiffnesses in the real beam onto effective longitudinally varying ones in the homogenized beam for the load case of non-uniform torsion.The focus of the numerical investigation, with consideration of the warping and Deformation Effect due to the Secondary Torsional Moment (STMDE), is on elastostatic analysis of straight FGM beams with rectangular hollow cross-sections. The influence of the variation of the material properties with respect to two or three directions on the angle of twist and the bimoment normal and torsional shear stresses is investigated. The obtained results are compared with the ones calculated by a very fine mesh of standard solid finite elements. This FGM warping non-uniform torsion beam finite element can be used not only in torsional analysis of general thin-walled beams but also in the design of FGM sensors and actuators in mechatronics.

Reduced model of macro-scale stochastic plasticity identification by Bayesian inference: Application to quasi-brittle failure of concrete

In this paper we deal with a probability-based scale bridging for concrete material when passing the detailed information at the meso-scale (the scale where the aggregate vs. cement microstructure is visible) with a Voronoi-cell based microstructure representation towards the chosen reduced model at the macro-scale (the scale where the concrete is a homogenized continuum) with a stochastic plasticity model for localized failure. This is accomplished by using Bayesian inference providing the probability distributions of the macro-scale model parameters expressed as random variables (RV) in order to compensate for the model reduction from the meso-scale, where parameters are expressed as random fields (RF). The original aspect of this approach is in the resulting macro-scale stochastic plasticity model, which can best quantify the uncertainty due to data loss in terms of the corresponding probability distribution of its parameters. The proposed procedure is illustrated in detail for the concrete meso-scale model presented in Part I of this paper (see Karavelić et al. (2019)), both for the simple elastic response, as well as for the plastic response with hardening in the fracture process zone (FPZ), followed by a softening response in the localized failure phase. This context of localized failure implies that the classical homogenization procedure no longer applies, and should be replaced by a macro-scale reduced model defined with respect to a quantity of interest (QoI), which is not necessarily the same for each particular response phase. The complete set of results for the parameter identification is combined together at the macro-scale in terms of a solid finite element with embedded discontinuity (ED-FEM), granting it very powerful predictive properties. The particular choice of ED-FEM for the macro-scale reduced model allows one to compute the QoI at an element-level, either as strain energy for the elastic response, or as plastic dissipation for each failure mode. Thus, the Bayesian inference computation of the probability distributions of the RVs representing the macro-scale model parameters, performed by matching such QoI results computed for the macro-scale and the meso-scale models, reduces to a homogenization-type procedure within a probabilistic setting that can successfully handle any case where the separation of scales no longer applies.

Forced vibration analysis of composite-geometrically exact elliptical cone helices via mixed FEM

In this pioneering study, the cross-sectional warping included transient response and normal/shear stress components of composite elliptical and elliptical cone helices over exact axis geometry are investigated using a mixed FEM. The transient analysis is performed using the Newmark time integration algorithm with or without the amplitude decay factor. The constitutive equations of composite curved rods are derived from three-dimensional elasticity theory. A displacement-type finite element formulation computing the warping-included torsional rigidity is incorporated with the mixed finite element formulation. The curvatures and displacement-type finite elements are used to estimate the normal and shear stress distributions on the respective cross-sections. The maximum normal/shear stresses of a composite straight beam are compared with the literature. An excellent agreement is obtained for the results of an exact elliptical cone helix under dynamic loads compared to the results of 3D solid finite elements. During the implementation of the time integration scheme, the first and second time derivatives of forces and moments are preserved, and their time histories are discussed. Finally, the influences of helix geometry, lamination, and the ratios of material constants on the transient response besides the stresses are investigated. All the numerical examples in this paper are original for the literature.

Deep learned finite elements

In this paper, we propose a method that employs deep learning, an artificial intelligence technique, to generate stiffness matrices of finite elements. The proposed method is used to develop 4- and 8-node 2D solid finite elements. The deep learned finite elements practically pass the patch tests and the zero energy mode tests. Through various numerical examples, the performance of the developed elements is investigated and compared with those of existing elements. Computation efficiency is also studied. It was confirmed that the deep learned finite elements can potentially outperform existing finite elements. The proposed method can be applied to generate various types of finite elements in the future.

Nonlinear finite element analysis of reinforced concrete flat plate punching using a thick-shell modelling approach

The punching shear resistance of reinforced concrete flat plates is an area where design is typically done in a highly-idealized manner, using provisions developed from experimental results of isolated slab-column connections; yet, involves structures where performance may be greatly impacted by system-level response. This paper presents the development and application of a practical thick-shell finite element-based nonlinear modelling procedure for reinforced concrete flat plate slab systems. Cracked concrete material modelling based on the formulations of the Disturbed Stress Field Model is employed in conjunction with computationally-efficient layered thick-shell finite elements that accommodate through-thickness shearing effects and are shown to be capable of capturing brittle punching-governed failure modes. A simple low-cost sectional analysis modification procedure is proposed to incorporate strength enhancements attributed to confining effects stemming from disturbances in slab-column connection regions. Load-displacement responses and failure modes developed using the proposed modelling procedure are shown to capture observed experimental responses and provide response estimates similar to those obtained using more costly three-dimensional solid continuum finite element modelling techniques. Finally, the analysis results presented were developed using simple-to-define concrete property input without the need for supplemental material model or analysis parameter calibration.

Research on the Simplified Calculation Model of Large Phased Array Radar Reflector Mechanics Based on NASTRAN

there are many plates and beams on the radar array. In the process of finite element calculation, choosing the appropriate shell mesh finite element model to replace the solid finite element model can reduce the calculation amount. In this paper, the finite element solid mesh model is established based on the reflection panel model of a radar antenna array, and the simulation results are obtained. Secondly, the shell grid is used to perform finite element modeling and correction calculations on the reflective panel. The results show that the modified shell grid calculation results are very close to the solid grid model results, and can replace the solid grid to simplify the calculation of the array.

Determination of the Bending Properties of Wire Rope Used in Cable Barrier Systems.

This paper presents research on the bending properties of 3 × 7 19-mm wire rope commonly used in road cable barriers. A total of 19 experimental tests were conducted. In addition, two nonlinear 3D numerical models of the wire rope using beam and solid finite elements were developed. Based on these models, four numerical simulations were carried out. The numerical results were validated against the experimental ones and a very good agreement was obtained. The main result of the research is the determination of the moment–curvature relationship for the wire rope considered. The effect of prestretching on the rope performance is discussed. The numerical results are analyzed in this paper in detail, including the behavior of the wire rope under bending and analyses of the cross-sectional and contact stresses. Suggestions concerning the type of finite element for wire rope modeling are also given. The results can be used, for example, in numerical simulations of crash tests of cable barriers.