Nonlinear Finite Element Calculations Research Articles

MODELING OF STRESS-STRAIN STATE AND STRENGTH OF DAMAGED CONCRETE BEAMS REINFORCED WITH CARBON FIBER FABRIC IN PC "LIRA-SAPR"

The study examines the problem of preserving and improving the architectural heritage in Ukraine. Many buildings and structures have a long service life or are already deteriorating due to their age and other factors. This is particularly true for reinforced concrete structures, which often have various defects and damage. Unfortunately, there are no clear methods for assessing the residual load-bearing capacity of such structures. However, the research indicates that the residual potential of damaged elements may be significantly underestimated. Therefore, it is crucial to explore and apply effective innovative solutions for strengthening these constructions. One such solution involves using composite materials (fiber-reinforced polymers, FRP) for external reinforcement of structures. Composite materials offer numerous advantages, including high strength, low weight, resistance to aggressive environments, and durability. The article presents the results of a numerical experiment aimed at investigating the influence of damage and reinforcement with carbon fiber-reinforced polymer (CFRP) on the stress-strain state and residual load-bearing capacity of concrete beams with basalt-plastic reinforcement (BFRP). For the experiment, 15 rectangular beams with dimensions of 2000×200×100 mm were prepared and nonlinearly analyzed using the "LIRA-SAPR" software, which employs the finite element method. The data obtained for each beam were compared with the results of laboratory tests, revealing that CFRP reinforcement increases the residual load-bearing capacity of the beams without significantly affecting their working deformation. Additionally, a comparative analysis was conducted on the residual load-bearing capacity and stress-strain state of the beam components: CFRP fabric, concrete, and reinforcement. The authors assert that modeling the complex stress-strain state of experimental basalt-concrete beams using nonlinear finite element calculations through the "LIRA-SAPR" software accurately reproduces experimental results, provides insight into the most likely failure mode, and reliably predicts their load-bearing capacity.

Eco-Resilient (ECORE) Concrete Constructions: A New Challenge and A New Concept

This paper presents a new concept concerning the development of eco-resilient concrete constructions, that is to say constructions with a reduced carbon footprint and which can withstand mechanical stress and physico-chemical attacks worsened by climate change. After a critical analysis of current research and development policies in the field of concrete construction, a new global approach is proposed which should allow this concrete construction profession to better respond to the challenges caused by global warming. This approach is based on two strong ideas a) The use of fiber concretes in combination with passive or active reinforcements in all constructions susceptible to crack b) The use of numerical models based on non-linear finite element calculations in order to optimize the design of eco-resilient concrete constructions.

Enhancing compressive performance in 3D printed pyramidal lattice structures with geometrically tailored I-shaped struts

This study examines the compressive response of geometrically tailored pyramidal lattice structures composed of struts with I-shaped cross-sections. Geometrically tailored pyramidal lattices with micro-scale features are 3D printed using the Digital Light Processing (DLP) technique, and their effective elastic modulus, collapse strength and energy absorption capacity are experimentally evaluated under quasi-static compressive loading. Furthermore, detailed non-linear finite element (FE) calculations are performed to examine underlying collapse mechanisms and explore the vast design space offered by the proposed geometrical tailoring scheme. Both the experimental and numerical results show that the geometrically tailored lattice structures outperform conventional pyramidal lattices of equal weight in terms of elastic modulus (+24 %), collapse strength (+21 %) and energy absorption (+68 %). Notably, these strength improvements are attributed to lateral buckling that prompts the I-shaped struts to bend sideways during collapse. Specific cross-sectional designs demonstrate remarkable enhancements in strength and energy absorption, reaching up to 93 % and 161 %, respectively, differentiating them significantly from conventional designs.

Quantitative reliability measures determination of a steel-reinforced concrete beam taking into account fatigue damage accumulation in flexible pin stops

Reliability is one of the most important properties of road bridges due to their degree of responsibility and strategic importance for the transport system. For steel-reinforced concrete bridges, which are widespread nowadays, the question of their overall structure reliability dependence on the element’s condition of steel beam and reinforced concrete slab connection remains not fully studied. The authors have performed fatigue damage accumulation numerical modelling in the conjunction elements of steel-reinforced concrete beam from the cyclic temporary loads influence and analysed this process influence on the overall structure reliability. Based on the previous studies data, a relationship model between the conjunction element shear rigidity and the amount of damage accumulated by it is proposed. The nonlinear finite element calculation algorithm with regard to the conjunction element’s rigidity reduction is proposed and tested on the model of the steel-reinforced concrete superstructure. The selection method of the equivalent time load for modelling the accumulation of fatigue damage process from traffic flow is proposed. In order to optimise the computational resources used it is proposed to use loading process clusterization into enlarged cycles groups and the rational group size is determined. A numerical experiment on the simply supported steel reinforced concrete beam model with different loading cycles number (from 1 loading to 100 million loading cycles) to determine the reliability index β under the assumption of variability of two parameters — design steel resistance and the value of temporary load. FORM (First Order Reliability Method) was used for probabilistic analysis. The study results have shown that the accumulation of fatigue damage in the elements of steel-reinforced concrete superstructures has a significant effect both on the load-bearing capacity of the superstructure beams and on the quantitative indicators of structural reliability (increase in the probability of structural failure, decrease in the reliability index β).

Determination of NSC-UHPC interface properties for numerical modeling of UHPC-strengthened concrete beams and slabs

Normal-strength concrete (NSC) structural components strengthened with ultra-high-performance concrete (UHPC) overlays are widely studied and have demonstrated their efficiency in improving structural capacity and durability. The behavior of UHPC-strengthened beams or slabs is highly influenced by the properties of the NSC-UHPC interface. This project aimed to develop NSC-UHPC interface models by determining their detailed shear and tensile laws in UHPC-strengthened beams or slabs, which are missing presently in the literature. Determination of the interface models was realized through test data analysis of 700 interface characterization specimens found in the literature and inverse analysis with nonlinear finite element (FE) calculations of 14 UHPC-strengthened beams and slabs test results. Two interface models were proposed for two types of interfaces with good or poor surface preparations, respectively: a concrete fracture (CF) model and an interface sliding (IS) model. Results showed that FE calculations with CF and IS models provide accurate replication of the mechanical behavior of strengthened beams and slabs in terms of stiffness (K), ultimate shear capacity (P), and deflection at ultimate shear capacity (Δ), while the calculations with perfect bond model were not satisfactory. Parametric studies on the nine interface parameters indicated that peak cohesion stress, shear stiffness, and tensile stiffness greatly impact the shear behavior of strengthened beams in the CF model, while only shear stiffness had a significant effect on the shear behavior of strengthened slabs in the IS model. Suitable choices for interface model parameters, as in the proposed CF and IS models, provided accurate results for modeling the bending and shear behaviors of UHPC-strengthened concrete beams or slabs.

Surrogate analytical models of damage localization in metal matrix composites

Several parameters entering the constitutive laws of metal matrix composites are not amenable to direct measurement. Their determination is therefore demanded to indirect identification procedures, based on the comparison between the output of some experimental works and the results of the iterative simulation of the performed tests. Largely repetitive numerical analyses can also support the optimized design of composite microstructures, the understanding of the actual stress-transfer mechanisms, and virtual testing. Surrogate analytical models can replace effectively non-linear finite element (FE) computations in parametric studies and identification procedures, reducing execution times and costs without compromising the accuracy of the results. In this context, a frequently used approach consists of the interpolation, by means of radial basis functions (RBFs), of data filtered by proper orthogonal decomposition (POD). This methodology is often used to reproduce the smooth output of different mechanical systems. This work is rather focused on the homogenized response of damaging metal matrix composites subjected to strain localization phenomena, and explores the accuracy achievable in these situations by the POD-RBF approximation of more traditional FE analyses. In all considered cases, the POD-RBF results are accurate, and able to distinguish between apparently similar situations. The approach is flexible, and the performance of the surrogate models can be tailored to the requirements of each application. In particular, various analytical approximations can be introduced to support the design of new microstructures and material couplings, and to understand the role of any material and/or geometry imperfections resulting from the production processes.

Analytical and numerical study of the lateral buckling of an imperfect pipe accounting for torsional effects

The stability problem of pipelines under high temperature and high pressure in terms of lateral buckling has been largely concerned recently. Owing to the complex conditions encountered in the sea bottom, many factors affect the structural behavior of pipelines resting on the seabed, such as initial imperfections and unexpected torsion. This paper thus focuses on the mechanical response of imperfect pipes (with a fixed length) under uniaxial compression, in presence of torsional effects. The problem is addressed first in an analytical way. The classical governing equations of a beam lying on the seabed are adjusted, introducing extra terms accounting for initial imperfections and twisting effects. The cases of imperfect pipes with free and fixed torsion at both ends are investigated, and closed-form analytical solutions are obtained in most cases. Furthermore, non-linear finite element computations are performed. Results include force–displacement response curves and buckled deformed shapes. A detailed comparison is conducted between numerical results and analytical solutions, accounting for various lateral stiffness densities, and different imperfection types and amplitudes. A general good agreement is achieved, at least within a small deformation domain. However, the numerical calculations sometimes lead to unexpected phenomena that analytical solutions cannot capture due to geometric non-linearities.

The effect of cross-section geometry on the lateral–torsional behavior of thin-walled beams: Analytical and numerical studies

In this paper, the elastic lateral–torsional behavior of simple beams is discussed by presenting a novel analytical solution and performing numerical studies. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, significantly different when the second-order nonlinear behavior of beams with initial imperfections is analyzed. To understand and explain the observed differences, a novel analytical model is worked out for the geometrically nonlinear analysis of beams with initial geometric imperfections. The advancement in the presented analytical solution is the explicit consideration of the changing geometry as the load increases. The most important steps of the derivations are summarized, and the resulting formulae are briefly discussed. The derivations are done for general cross-sections, however, the bending is assumed to act in one of the principal planes. Numerical studies are also presented, focusing on mono-symmetric cross-sections. As part of the numerical studies, first, the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae can capture the most essential elements of the behavior observed in the shell finite element calculations, justifying that the cross-section shape might have a significant effect on the nonlinear lateral–torsional behavior of beams. Then the effect of the lateral–torsional buckling is predicted by calculating buckling reduction factors, using the results of the geometrically nonlinear finite element calculations. The capacity prediction results, again, justify that the cross-section shape, as well as the sign of the assumed geometric imperfection, might have a non-negligible effect on the buckling reduction factors, and on the capacity of the member.

Redistribution of internal forces from the span to the support

AbstractThis paper presents the results of evaluations on the redistribution of internal forces from the span to the support area using nonlinear finite element calculations. The motivation is the internalization of bridges, particularly the reconstruction of single‐span beams arranged in a row to a continuous beam system. When integralizing a bridge, it can be assumed that the existing bridge is designed according to standards, which are no longer valid. If the integralized bridge is loaded and designed according to the new standard, the problem may be that the existing structure has insufficient reinforcement. For single‐span bridges, the flexural reinforcement in the span may be considered critical. The degree of reinforcement in the support area can then be adjusted individually, which offers the possibility of transferring internal forces from the span to the support area if they cannot be fully absorbed by the existing reinforcement.

Data-driven finite element computation of open-cell foam structures

This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem.The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open-cell microstructure and the properties of the polyurethane material. Their computation provides the required stress–strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to derive suitable material data sets for the different cases of (non-)linear and (an-)isotropic material behavior efficiently.Exemplarily, we compare data-driven finite element computations with linearized and finite deformations and show that in a data-driven computation the linear kinematic is sufficiently accurate to capture the material’s non-linearity up to 50% of straining. The numerical example of a rubber sealing illustrates possible areas of application, the expenditure, and the proposed strategy’s versatility.

Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

In this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to near equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion (15) which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation (48). From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. (42) –which investigated materials with yielding described by the orthotropic criterion of Hill (24)– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s− 1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations.

Model Order Reduction for Real-Time FPGA-Based Finite Element Transient Simulation of Three-Phase Transformer

The finite element method (FEM) is commonly used in modeling the electromagnetic field of transformers with high accuracy; however, the computation time of the FEM is prohibitively high for real-time simulation due to high model order. Reducing the model order is helpful to improve the computational efficiency of the FEM. The proper orthogonal decomposition (POD) is an efficient method to reduce the linear model order but encounters difficulties with nonlinear models. In this paper, a model order reduction (MOR) method based on the combination of POD and the transmission-line modeling (TLM) is proposed to reduce the nonlinear finite element model order and computation time. The TLM method is used to separate the nonlinear components from the model, and then the POD is used to reduce the linear domain order of the model. The nonlinear components obtained by TLM can be solved in parallel on the field programmable gate array (FPGA) to improve computational efficiency further. This paper has studied the transient states of a three-phase transformer with the current excitation and field-circuit coupling. The real-time hardware emulation results are validated by results from offline simulation using Comsol®.

Study on deformation of abutment and the influence on high arch dam during impoundment

High arch dams in China have been impounded and entered the operation stage in succession. The value and law of deformation during impoundment are different, which brings a great challenge to the performance and long-term safety of the arch dam. Based on the analysis of monitoring data of Jinping No.1 arch dam and Xiluodu arch dam, it is pointed out that the valley width deformation is irreversible plastic deformation, and there are two modes of valley width deformation of dam foundation: bank slope deformation mode and overall deformation mode. The bank slope deformation mode shows that the valley width of the upstream is significantly larger than that of the downstream, and the chord length of the dam is not large. Based on the principle of effective stress, the deformation mechanism of bank slope deformation mode is discussed. The overall deformation mode shows that the valley width of the upper and lower reaches is similar and the magnitude is large, and the chord length of the dam is large. The boundary displacement method is used to simulate the overall deformation mode. The model of Baihetan arch dam is established, and the structural model and geological conditions of the dam site are simulated in detail. Based on 3D nonlinear finite element calculation, the effects of two valley width deformation modes on the displacement, stress and local cracking of Baihetan arch dam are analyzed, and the calculated results are compared. The results show that the overall deformation mode can cause infinite valley width deformation, while the bank slope deformation mode can only cause limited valley width deformation. When the same valley shrinkage value is produced, the bank slope deformation mode can make the dam produce new stress concentration area, and the overall deformation mode has little effect on the dam stress, which indicates that the non-uniform deformation of the dam foundation is the key to affect the stress in the dam.

A new type of wind-resistance cable net for narrow suspension bridges and wind-resistance cable element for its calculation

In this paper, a new-style cable net structure consisting of a wind-resistance main cable, wind-resistance secondary cable and pulleys is proposed to improve the wind-resistance stability of narrow suspension bridges. In the improved structure, the wind-resistance secondary cable which slides on pulleys to achieve uniform distribution of cable force. However, the calculation for this structure is very difficult due to the sliding cable, which means the unstressed length of the cable between the pulleys is not fixed. To this end, a multi-node wind cable element considering the cable sliding on nodes is proposed for the wind-resistance secondary cable. Additionally, an analytical model of the wind cable element is established according to the structural features. The unstressed state method, virtual work principle and influence matrix method are all used to deduce and verify the tangent stiffness matrix of the element. As a result, the exact nodal forces can be calculated according to the static equilibrium conditions and the proposed element implemented for the nonlinear finite element analysis of the suspension bridge. Numerical and bridge examples are used to demonstrate that the new element can successfully simulate the sliding of the cable on the pulleys, and be applied to the nonlinear finite element calculation like any normal element. By means of this method, a wind-resistance secondary cable with any cable section connected by pulleys to the wind-resistance main cable and stiffening girder, can be accurately simulated with only one wind cable element. Hence, the calculation problem of the wind-resistance cable is resolved and overall calculation accuracy and efficiency are improved.

Design model for bolted angle members in compression including joint stiffness

Knowledge of type and size of rotational restraints at the member's ends (provided by the adjacent structure) is crucial for the prediction of the compression member capacity of bolted angles. This was highlighted by means of experimental and numerical investigations in the past. Due to the eccentric connection on only one angle leg, additional bending moments are acting on the member, leading to a complex load carrying behaviour with flexural and/or lateral torsional buckling phenomena.Detailed analytical models for the estimation of appropriate spring stiffness values have been developed for several practical applications in buildings with two-bolt connections at both member's ends. The investigated connection details comprise a simply fixed gusset plate (e.g. as attachment to concrete walls), a joint to the flange of an I-shaped section and a joint to the web of an I-shaped section via a gusset plate. Based on that, a design model was developed for bolted angle members with rotational spring restraints at the member's ends and an eccentric compression loading N, in order to calculate the compression capacity NR. The thereby determined resistances NR,model are compared with the results of sophisticated 3D nonlinear finite element calculations NR,FE that consider the detailed joint configuration and the eccentric load introduction as well as equivalent geometric imperfections. It is shown that the resistances based on the proposed design procedure are slightly conservative compared to the real behaviour of the angle member. In addition, the large increase in capacity (compared to the simply supported reference case) is highlighted.

Experimental research on four-point-bending loading of composite fuselage frame

A four-point-bending loading test device was designed for the pure bending loading of the composite fuselage curved frame. The reinforcing subplates, reinforcing frames, wedge-shaped blocks and other parts were installed in the load segment of test pieces to enhance the local stiffness, strength and torsional stiffness. Four-point-bending loading tests and nonlinear finite element calculation of C-frame and Z-frame pieces under the condition of positive bending was carried out. The calculated buckling mode was in good agreement with the test result, which provides a certain theoretical basis for the instability mode analysis of curved frames. The test and analysis results show that under the condition of positive bending and the middle section of C-frame has lateral instability and the end inner edge of the frame has the local buckling and damage. While the middle section of inner edge of the Z-frame has only local buckling and damage. The test results of two kinds of frame show that the stability and structural strength of Z-frame are better than that of C-frame.

Snap-through of bistable variable stiffness laminates using MFC actuators

Unsymmetric composite laminates exhibit two or more stable equilibrium shapes with opposite curvature as a result of residual thermal stresses induced during the curing process. Surface bonded Macro Fibre Composite (MFC) actuators are generally employed to trigger snap-through between one stable shape to another by applying external voltages. However, these actuators require high actuation voltage input to change from one stable shape to another, especially when used in morphing applications. If the snap-through voltage is too high, morphing becomes infeasible or may require several actuators, which is contrary to the weight requirements. Variable Stiffness (VS) laminates provide the possibility for an enlarged design space with the possibility to tailor stiffness parameters, leading to lower snap-through loads and consequently reducing the size of the actuators.On the prediction of snap-through voltages, the existing semi-analytical models have shown reasonably high discrepancies between numerical and experimental results. An improved analytical model is proposed in this study to predict the snap-through of bistable VS laminates with MFC actuators. In the improved model, the equations resulting from the compatibility and the in-plane equilibrium are described equivalent to a standard plane elasticity problem which can be solved using a standard finite element (FE) approach. In addition, the total potential energy is written in terms of curvatures. The improved semi-analytical results are compared with a full geometrically nonlinear FE calculation.

Feasibility analysis of semi-welded seamless turnout in Yuqomolangma Station of Qinghai-Tibet Railway

It is difficult to lay seamless turnouts on the Qinghai-Tibet Railway, and the large temperature difference between day and night on the plateau railway leads to large changes in the temperature of the turnouts. Aiming at the equipment status of No.1 turnout in the Yuzhufeng station of the Qinghai-Tibet railway, a non-linear finite element calculation model of P60-12 single-open turnout was established. The long rail was calculated and analyzed based on the construction lock rail temperature and the local maximum and minimum rail temperature. The development law of displacement under temperature changes, after comparing the field measured displacement observation data, the model calculation result is correct, and the lateral displacement meets the requirements. Comparing and analyzing on-site rail displacement observation data, the model calculation results meet the engineering accuracy requirements. In the season of the highest rail temperature in the year, strain sensors are installed at the rail waist at different parts of the semi-welded seamless turnout to collect the rail strain increment under the cyclic change of rail temperature. According to the strain increment change rule, displacement observation data and model calculation results, it is concluded that the scheme of laying a semi-welded seamless turnout in Yuqomangma station is feasible, and the rail in the bifurcation area is stable under the action of temperature stress.

An artificial intelligence approach to model nonlinear continua by intelligent meta‐elements

AbstractA data‐driven “intelligent” meta‐element that reduces the dimensionality and accelerates nonlinear finite element computations is demonstrated on an elastoplastic continuum frame.

Stochastic geometric imperfections of plate elements and their impact on the probabilistic ultimate strength assessment of plates and hull-girders

The present paper proposes a novel approach for the representation of the imperfect plate geometry of ships structures and assess its impact on the probabilistic ultimate strength of plates and hull-girders. The description of the imperfect geometry is basically implemented using the theory of random fields. Evidence for the selection and robustness of the proposed model is documented from literature data and real measurement campaigns conducted on ships. A preliminary study is first presented upon the prediction of plates’ probabilistic ultimate strength comparing the efficiency of the proposed model with existing imperfection models from literature. Afterwards, a case study on a VLCC oil tanker for the prediction of hull-girder ultimate strength applying different imperfection models takes place. In order to evaluate the variability of ultimate strength under the effect of stochastic imperfections, artificial neural networks (ANNs), which trained appropriately with relatively limited results of non-linear finite element calculations, are used. The main objective of this research study is to provide a methodology for the evaluation of probabilistic-based ultimate strength assessment of plates and hull-girders in view of stochastic geometric imperfections. In doing so, and incorporating other sources of uncertainties, the designer/engineer should be able to perform a valuable reliability-based analysis of the structure.