Arc-length technique for nonlinear finite element analysis

Computer Methods in Applied Mechanics and Engineering, 1979

Due to the corrosion that occurs in internal steel reinforcement; many of steel reinforced concrete structure are at risk of collapse. The budget that will be developed to address this risk in terms of replacement or repair of damaged concrete structures will be very high for the owner or responsible authorities. Alternatives to bare steel have been used including stainless steel, galvanized steel, epoxy-coated steel and cathodic protection, with limited effectiveness. The characteristics of fiber reinforced polymer (FRP) bars like the high tensile strength, inability to corrode, and light weight; it has become the focus of decision-makers to use it instead of steel in internal reinforcement for future concrete structures. In this research, we have investigated flexural behavior in reinforced concrete beams with bars from bars from carbon fiber-reinforced polymer (CFRP), bars from high tensile steel (HTS), and glass fiber-reinforced polymer (GFRP) under static load. Two groups from samples were used, in the first group will show the effect of the type of reinforcement. In the second group will show the effect of the type of reinforcement with different concrete strength. It found these kinds of materials to be very is effective to deal with analysis and the proposed simulation of the material in this study are able of forecast the real behavior of reinforced concrete beam by FRP bars in terms of failure load, and loaddeflection behavior.

Defence Technology, 2019

The article demonstrates a novel approach for material nonlinear analysis. This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior. It is found that the methodology is very suitable to apply for the brittle material such as concrete and composite materials. One dimensional problem of a simple bar is solved to formulate fundamental procedure and basics of the method. Another two dimensional problem of beam bending is solved for further strengthening the method. It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results, easy to adopt and simple in calculations. The method not only eliminates linearity assumptions in its derivations and calculations but also eliminates all types of possibility of errors in the analysis procedure.

An analytical model, which can simulate the biaxial description of the nonlinear behavior of reinforced concrete structures, is introduced. The behavior of concrete is assumed orthotropic inside the ultimate failure surface and a compressive softening law of concrete is presented. The behavior of cracked concrete is simulated using the smeared crack model, which the tension stiffening effect based on a cracking criterion derived from the fracture mechanics principles is considered. A computer program is developed for analyzing the over and under-reinforced concrete beams. Several parameters such as the non-linearity proprieties, the cut off and tension stiffening models and shear retention factor are studied. The correlation between analytical and experimental results shows the validity of the proposed models and the significance of various effects. The global responses are evaluated to verify simultaneously the reliability of the proposed model and the performance of the numerical program.

Computers & Structures, 1989

Solution capabilities for three-dimensional geometric and material nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including triaxial nonlinear stress-strain behavior, tensile cracking, compression crushing and strain-softening. The objective in this work was the development of a practical nonlinear concrete analysis capability. The material model can also be employed to represent some rock materials. The results of various sample analyses are given, in which the stability and accuracy of the finite element representations have been studied.

The non-linear behavior of reinforced concrete (RC) beams till the ultimate failure is a complicated phenomenon due to the involvement of heterogenic material properties and cracking behavior of concrete. Behavior prediction of reinforced concrete elements till failure is usually carried out using experimental testing, and the observations are recorded only at critical locations due to restriction in cost of testing equipment and accessories. In order to avoid the destructive testing, reduction of the cost of materials and manpower, the behavior prediction of RC beams is generally carried out using numerical methods. This paper presents study on non-linear flexural behavior of reinforced concrete beams. Non-linear finite element analysis of reinforced concrete beams under flexural loading is presented in this paper. Finite element modelling of reinforced concrete beams is carried out using discrete reinforcement modelling technique. The capability of the model to capture the critical crack regions, loads and deflections for various loadings in reinforced concrete beam has been illustrated. Comparison is made between the experimental results and finite element analyses with respect to initial crack formation and the ultimate load capacity of beams. The results obtained in the present study show close agreement with those in the available literature.

Revue européenne des éléments finis, 2004

An analytical model, which can simulate the biaxial description of the nonlinear behavior of reinforced concrete structures, is introduced. The behavior of concrete is assumed orthotropic inside the ultimate failure surface and a compressive softening law of concrete is presented. The behavior of cracked concrete is simulated using the smeared crack model, which the tension stiffening effect based on a cracking criterion derived from the fracture mechanics principles is considered. A computer program is developed for analyzing the over and under-reinforced concrete beams. Several parameters such as the non-linearity proprieties, the cut off and tension stiffening models and shear retention factor are studied. The correlation between analytical and experimental results shows the validity of the proposed models and the significance of various effects. The global responses are evaluated to verify simultaneously the reliability of the proposed model and the performance of the numerical program.

Journal of Structural Engineering, 2014

Revista IBRACON de Estruturas e Materiais

This work aims to investigate the ultimate capacity of reinforced concrete elements in terms of cracking and stiffness loss. Nonlinear finite element analysis (NLFEA) was performed in the ATENA software and compared with a proposed numerical simulation of nonlinear static analysis (NLSA), where material cracking is evaluated based on the loss of tangent stiffness of the elements. The analysis was applied to a low-rise reinforced concrete frame with constant axial loads in the columns, and monotonic lateral load applied at the top beam level. Both methodologies showed good agreement regarding the capacity curve and crack patterns, and the numerical simulation NLSA allowed the identification of the sequence of elements' stiffness loss. The results indicated a substantial similarity between the numerical simulation NLFEA and NLSA and the experimental test, indicating a high potential in predicting the nonlinear behavior of reinforced concrete.

Tikrit Journal of Engineering Science, 2009

This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1) with enhanced shear interpolation will be used in this study. Table (1) describes shape functions and their derivatives of this element. An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10) have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiati...

One of the significant difficulties in representing the behavior of reinforced concrete structures in mathematical models is the postcracking non-linearity. And so, reinforced concrete slabs are no exception to the rule. Still, the usual analysis models for this structural element are verified in the elastic regime when the concrete tensile strength is considered. This model is acceptable for the service limit states but not the ultimate limit state. These aspects associated with the great difference in the behavior of concrete when subjected to tension or compression make it necessary to study a nonlinear mathematical model that can represent a reinforced concrete slab subjected to bending, from the beginning of loading until its failure, as accurately as possible. With this, the ANSYS software, from its version 18, made available in its library the Drucker-Prager-Rankine model arranged with two distinct rupture surfaces. A Drucker-Prager criterion for the concrete subjected to compression and a Rankine criterion for concrete in tension. In addition, the software is based on the finite element method, giving the possibility of precise and nonlinear analysis through load and deformation increments, taking into account both elastic and plastic deformations after concrete cracking. Thus, this work aims to present the modeling of reinforced concrete slabs through the Drucker-Prager-Rankine surface, validating the model by comparing it with several experimental tests. The model results were coherent and acceptable, presenting a good approximation of the results of the tests.