Plane Stress Elements Research Articles

An interface-based microscopic model for the failure analysis of masonry structures reinforced with timber retrofit solutions

This paper presents a refined Finite Element (FE) modeling strategy for analyzing the failure behavior of regular masonry structures reinforced with timber-based retrofit solutions. The proposed model schematizes the masonry as brick units, modeled using two-dimensional linear elastic plane stress elements, mutually joined through zero-thickness cohesive interface elements. These interface elements serve to reproduce the nonlinear behavior of masonry because of the occurrence of failure mechanisms of the mortar joints. Reinforced timber frame elements are modeled using truss elements that exhibit elastic brittle fracture behavior. The interaction between the masonry sub-structure and the reinforced timber frame system is accounted for using special constraint conditions that simulate the mechanical behavior of anchorage connections. The reliability of the proposed model in reproducing the failure behavior of masonry is assessed through comparisons with experimental and numerical data available in the literature. Additionally, the efficacy of the retrofit technique based on timber frame structures is investigated in detail through pushover analyses on a two-story masonry wall representative of real-life masonry buildings. The results indicate that the proposed retrofitting strategy is an effective and eco-friendly retrofit solution to enhance the in-plane bearing capacity of masonry structures subjected to horizontal forces.

Alternative Low-Order Triangular Elements for Thick and Thin Shell Analysis

In this paper, the authors discuss the development of six low-order triangular elements for the linear static analysis of thick and thin shell structures. The elements combine two triangular plane stress elements with three triangular thick plate bending elements to produce three-node flat shell elements with 18 degrees of freedom. The two plane stress components are based on the free formulation and the template formulation, while the three plate bending components are based on the free formulation, the deviatoric strain formulation and the hybrid-Trefftz formulation. The theoretical backgrounds and formulations of all elements are briefly discussed to provide a concise summary, while further details are given in the quoted references. The elements are used to analyze five standard shell benchmark examples, and the results obtained are compared to previous work in this area. The elements provide accurate and robust results for the benchmarks, with only small differences for the results as the meshes are refined. While all the proposed elements can be recommended for general shell analysis, the combination of the template plane stress element and the hybrid-Trefftz plate bending element generally provides the best results.

Unconventional cyclic plasticity model implementation for shell and plane stress elements in UMAT/Abaqus

Finite element simulations are widely used in several industrial sectors (civil, aerospace, mechanical, naval, biomedical, etc.) to design components or structures. Often, the resolution of highly non-linear problems requires the recurse to dense meshes with the consequent increase in computation time. This aspect becomes particularly relevant for cyclic mobility problems where repeated loading might affect the computational cost. Therefore, the efficiency of finite elements represents a crucial aspect of speeding up the design process. Past works of the authors focused on developing the additive hypoelastic-based and multiplicative hyperelastic-based constitutive equations of the Extended Subloading Surface model for three-dimensional finite elements adopting fully implicit integration schemes. In this paper, the constitutive equations of the Extended Subloading Surface theory are reformulated for shell and plane stress elements, aiming to obtain an efficient computational tool suitable for cyclic mobility problems. The numerical implementation considers isotropic hardening, kinematic hardening, and material anisotropy. Numerical solutions obtained utilising shell/plane stress and solids elements are also discussed.

Evaluation of Piezoelectric-based Composite for Actuator Application via FEM with Thermal Analogy

In the present work, a new study on the piezoelectric-based structure by means of Finite Element Method (FEM) is conducted. Currently, the piezoelectric model in the FEM-based commercial software is only applicable via 2D plane stress and 3D solid elements. However, piezoelectric structures are usually manufactured as thin-walled structures, i.e., plates and disks. Therefore, it is more convenient to model a piezoelectric-based structure with 2D shell elements. In this study, FEM with a thermal analogy approach is implemented. Thermal coupling characteristics are utilised as the equivalent of electromechanical properties. Thermal analysis is much more established in FEM-based software; thus, applications with various types of elements are enabled. Therefore, the evaluation of piezoelectric structure via shell element with a thermal analogy approach could be performed. Static and dynamic analyses are conducted with experimental and numerical validations. As depicted in some details in this paper, the shell model with thermal analogy shows an excellent agreement with the 3D solid piezoelectric elements with insignificant variances, less than 0.3%.

Comparative numerical study to simulate masonry with bed joint reinforced repointing

Bed joint reinforced repointing is a retrofitting technique for unreinforced masonry structures that is commonly applied in the Netherlands to repair settlement-induced damage. Using this technique, the bed joints of masonry walls are reinforced with steel rebars that are embedded in a high strength repair mortar. Due to the increase of induced seismic events in the northern part of the Netherlands, an experimental study was carried out at Delft University of Technology to investigate the performance of this retrofitting technique for combined settlement and seismic loading. This paper aims to simulate the experimental results, with a focus on the comparison of different finite element modelling approaches for studying both un-strengthened and strengthened full-scale tested walls. To that end, three different models are investigated – comprising both macro (continuum) and simplified and detailed micro (brick-to-brick) modelling approaches. The bricks and mortar joints are modelled as one homogenous continuum in the macro model, whereas in the two brick-to-brick models these structural components are modelled separately, with the detailed model including interface elements to simulate the brick–mortar bonds. Nonlinear pushover analyses are subsequently carried out using all three modelling approaches, for both monotonic and cyclic loading cases. Based on these analyses, the detailed brick-to-brick model was found unsuitable to simulate the strengthened wall because cracks in the model mainly occur in the form of opening of the brick–mortar bond interfaces, while smeared cracking in the plane stress elements of the mortar joints is very limited. Similarly, the continuum damage model was found to be inaccurate when pre-existing damage in the experiment needed to be taken into account. The continuum damage model also showed lower axial stresses in the rebars, compared with the simplified brick-to-brick model, as the former does not allow for the direct assignment of material properties for the high strength repair mortar in the strengthened joints.

Explicit Method in the Seismic Assessment of Unreinforced Masonry Buildings through Plane Stress Elements

The complex nonlinear behaviour of unreinforced masonry (URM), along with the interaction between structural elements, still represents a challenge for the seismic assessment of existing URM buildings. A large variety of mathematical tools have been developed in the last decades to address the issue. The numerical work herein presented attempts to provide some insights into the use of FEM models to obtain reliable results from nonlinear dynamic analyses conducted with explicit methods. Through plane stress elements, two in-plane mechanisms were studied to identify optimal parameters for unreinforced masonry elements subjected to dynamic actions. The results were then compared with outcomes generated by an implicit solver. Subsequently, these parameters were used in nonlinear dynamic analyses on a building section for the seismic assessment in both unreinforced and reinforced conditions. The element type, hourglass control, damping, and bulk viscosity influence the dynamic response, mainly when the nonlinearities become larger. The hourglass control techniques employ a scaling factor to suppress the occurrence of spurious modes. Values ranging from 0.01 to 0.03 have shown effective results. When the stiffness-damping parameter for Rayleigh damping is of a similar order of magnitude or lower than the time increment without damping, the time increment remained in feasible ranges for performing analysis. Additionally, the bulk viscosity can stabilise the response without causing substantial alterations to the time increment if the values are under 1.00.

Nonlinear Static Pushover Analysis of Hollow Shear Critical RC Bridge Piers Under Monotonic Loading: A Comparitive Study

Hollow RC bridge piers exhibit several failure modes when subjected to extensive time varying loads during their service lives. Shear failure of hollow RC bridge piers is very critical as it is brittle in nature involving rapid deterioration of strength with increasing widths of the shear cracks and low ductility. Hence this type of failure is not desirable in the earthquake prone areas. Simulation models that can accurately predict the characteristic load deflection curve parameters (including yield load, peak load, ultimate load and corresponding drift, ductility and post peak strength degradation) are very much essential for efficient design of these structures. In the present study, a nonlinear static pushover analysis of three hollow rectangular RC bridge piers (one flexure critical and two shear critical) has been performed under monotonic loading using four different analysis techniques. The first type of simulation model used in the present study is based on the commonly used fiber based nonlinear beam-column elements with simple uniaxial material constitutive relationships, which are very effective in predicting the flexural response of bridge piers. The second type of simulation model used in the present study is also based on simple fiber based nonlinear beam-column elements. However, the constitutive relationships of steel in this model are modified to predict the post-peak strength degradation in shear critical bridge piers. The third type of simulation model is based on two dimensional (2D) CSMM based smeared RC plane stress elements. The fourth type of simulation model is an analytical model based on the sectional analysis method. The load deflection curve properties obtained from all the simulation models have been compared with each other and also with the experimental data. It has been concluded from the present study that all four models are equally efficient in predicting the behaviour of flexure critical bridge pier. However, in the case of shear critical bridge piers, predictions from the 2D CSMM based simulation model are more accurate.

Impact based characterization of composites using a computational framework

This article has employed a computational method to evaluate the dynamic response of Carbon fiber reinforced polymers composite material. Three Dimensional, Computational Shell and Two Dimensional modelling of a protective system has been conducted by the authors using Finite Element Method. In order to simulate the influence of space debris impacts on carbon epoxy composites, velocity variation in high and hyper speed range has been conducted. Rigid elements were utilized to model the projectile, while three dimensional stress elements, Continuum Shell elements and Plane stress elements were used for three dimensional, Continuum Shell and two dimensional modelling of the plate. The computational results indicated a good convergence with the available experimental results with variation less than 10%. It was observed that the generated stresses, energy absorbed, damaged area as well as the computation time of the models increased with the subsequent increase in impacting velocity. An increase of 75% in the energy absorbed, 86% increase in the generated stress and 93% increase in the deformation was observed against an increase in the impact velocity from 150 m/s to 1674 m/s. A maximum increase of 12% in the overall damage area, 41% increase in delamination of plies and 95% enhanced computation time was also observed against the above mentioned velocity variation.

On the improvement of four-node plane stress element

In this paper, a simple way is proposed to improve the overall performance of the four-node plane stress element. Numerical examples are given. Results show that the accuracy of both stress and displacement for a coarse mesh is raised by the proposed method. The reason is clearly given. The problem of mesh size dependent may be overcome in a certain degree if integration points are properly selected.

Solid isotropic material with thickness penalization – A 2.5D method for structural topology optimization

SIMP is the most common topology optimization scheme to minimize the material utilization of a structural component using element densities as a design variable. This paper presents a new methodology, SIMTP, Solid Isotropic Material with Thickness Penalization, introducing a nodal thickness variable to the plane stress element. SIMTP uses a 2.5D element, and it is developed considering the varying thickness as a 3D problem and planar transformation as a 2D problem. The developed 2.5D element is used for projecting the 2D strain energy onto a 3D space. Classical optimization problems like Cantilever, MBB, and L-, beams are solved using 2.5D SIMTP, and results are compared with SIMP. The implementation is simple, directly representing the thickness, and nodal design variables enhance the resolution. Checkerboarding or other topology-related issues are not noticed during the process. Also, 2.5D SIMTP can yield desired results with fewer elements, thereby reducing the computational efforts. Besides, a 211-line MATLAB implementation of 2.5D SIMTP with examples is provided at the end of this paper.

Dynamic evaluation of aluminum alloys using a virtual framework

This research paper has utilized a computational based approach to assess the impact response of Aluminum alloys. The authors have conducted Two Dimensional, Continuum Shell and Three Dimensional modelling of a shielding system using Finite Element Method. Effect of thickness and velocity variation has been emphasized with a view to simulate the effect of space debris on the metallic shielding system. Plane stress elements, Continuum Shell elements and Three Dimensional stress elements were used for Two Dimensional, Continuum Shell and Three Dimensional modelling of the plate, while rigid elements were used to model the projectile. The computational results showed a good agreement with the experimental results available. A maximum of 14 % increase in the relative damaged area of the specimen was observed, while the maximum stress generated under the impact was 395 MPa, leading to an immediate failure of the plate at a velocity of 1674 m/s. The numerical damage topologies also showed confidence with the published experimental results.

Modeling of ultra-high performance fiber reinforced concrete columns under eccentric loading

Recently, ultra-high performance fiber reinforced concrete (UHPFRC) has been widely used as a structural material. In this study, two finite element (FE) models are developed to investigate the behavior of UHPFRC columns under axial or eccentric loading. The analysis included two dimensional FE model using plane stress elements, and three dimensional FE model using solid elements. The FE models are verified using experimental results from the literature. It is proved that the FE models can predict the peak loads, modes of failure, and post-cracking behavior accurately. The FE interaction diagram agreed very well with the experimental results. The validated FE model is adopted to show the effectiveness of UHPFRC on the behavior of column versus using normal strength concrete (NSC) and high strength concrete (HSC). The FE results demonstrated that using UHPFRC improves the post peak ductility and increases the peak loads compared to those of NSC and HSC. Furthermore, a proposed simple analytical model is generated to predict the axial load-moment interaction diagram of UHPFRC columns and calibrated with both experimental and FE results. Comparing the analytical, experimental, and FE results showed that the proposed analytical model has comparatively high accuracy acceptable for practical design.

Predicting Behavior of Steel-Clad, Wood-Framed Shear Walls under Cyclic Lateral Loading

HighlightsA finite element analysis (FEA) model was developed to predict behavior of steel-clad, wood-framed (SCWF) shear walls under cyclic loading.This FEA model will be useful in determining post-frame building response to seismic forces.The model will save time and money in developing design coefficients and planning experiments for SCWF shear walls.Abstract. This article presents finite element (FEA) model results of steel-clad, wood-framed (SCWF) shear walls under cyclic lateral loading. The shear wall model consists of beam elements to model framing members, equivalent orthotropic plane stress elements to model corrugated steel cladding, linear spring elements to model nail connectors between framing members, and nonlinear hysteresis spring elements to model screw connectors. Screw connectors attaching steel panels to wood framing and steel panels to steel panels at lap joints were tested under cyclic loading to provide the constitutive relationships needed. A modified Bouc-Wen-Barber-Noori (BWBN) model was developed to capture slack, pinching, and strength and stiffness degradation of screw connectors under cyclic loading. The finite element models were validated by comparing them with experimental test results of six different SCWF shear wall configurations. Predicted peak shear strengths for most load cycles were slightly higher than those from the experimental tests, especially for stitched shear walls. Visual inspection of the FEA predicted hysteretic load curves demonstrated that pinching, and strength and stiffness degradation were well captured. The results of this study demonstrate the utility of the FEA model for comparative studies of different SCWF shear wall constructions under cyclic lateral loading. Keywords: Cyclic lateral loading, Diaphragm design, Post-frame building, Steel-clad wood-frame diaphragm.

Flexural behavior of basalt fiber reinforced concrete beams: Finite element simulation with new constitutive relationships

Concrete reinforced with fibers is widely utilized to attain noticeable durability in structures. Basalt fibers recently manufactured from igneous basalt rocks have been found to be extensively employed in concrete constructions around the world. The aim of this paper is designed to cover a comprehensive plan for examining the behavior of basalt fiber reinforced concrete (BFRC) beams under bending effect using finite element analysis, and introducing new BFRC constitutive relationships or models. Concrete was modelled by plane stress elements reinforced with embedded steel bars. New models for constitutive relationships were proposed to predict the performance of BFRC under tensile and compressive stresses and estimate its modulus of rigidity after cracking. These models were formulated based on the regression analysis of numerous experimental data compiled from the literature. Different constitutive relationships were proposed and devoted to model the strength of BFRC to the uniaxial compressive stresses, its stiffening to the tensile stress and transference of shear force within the cracked BFRC. The outcomes of present finite element simulation were verified via comparing them with the results of previous testing works in terms of the flexural strength, ductility, and cracking form of BFRC beams. This study reveals that the usage of the proposed elastic–plastic compressive behavior model of BFRC with the second quadratic model of its tension stiffening phenomenon shows minimum error (less than 3.0%) in the predicted behavior of BFRC beams.

Development of Finite Element Analysis for Intermediate Length Coupling Beams Considering Bond-Slip Interface

Finite element analysis is performed on four reinforced concrete coupling beams of intermediate length using 2-D plane stress elements, under monotonic load up to failure. The model is verified using the results from (Nabilah and Koh in KSCE J Civil Eng 21:2807–2813, 2017). The bond-slip interface for the longitudinal reinforcement is modeled in the finite element, as it is found that it better predicts the load-deformation behavior compared to perfect bond. The comparison between finite element analysis and the experiment found that the model is able to predict the overall behavior of the structure, especially the maximum load capacity. The maximum deformation and the shear deformation from the finite element analysis are found to be underestimated, due to the inability of the model to predict shear deformation accurately. Flexural deformation (due to flexure and slip) is found to be well predicted, as the bond-slip behavior is modeled in the analysis. Generally, the shear deformation and slip are found to be significant in the intermediate length coupling beam and should not be ignored in the analysis. Finally, the effective stiffness prediction using finite element analysis is found to be overestimated and should be determined instead using existing equations.

Statistical Analysis of Adhesive Bond Parameters in a Single Lap Joint System

The design and sizing of adhesives used for bonding of two or more similar/dissimilar materials in aerospace and automobile structural engineering studies have always been important. A vast number of studies have reported via experimental, numerical, and analytical methods of lap joint system with adhesive bonding. Optimization studies of the adhesives used in joints are highly necessary which can be done either with numerical or experimental data in determining the suitable parameters for the specified solution through the design of experiments analysis. In this study, a single lap joint with different variables has been modelled and the resulting stress was measured in each case. A standard two-dimensional plane stress element was used for modelling of single lap joint stress elements. Furthermore, a statistical analysis method was used to optimize the selected parameters for the improvement of current solutions with suitable parameters. The results showed that the response values of stresses were influenced by input parametric variables which control the stresses and reduces the risk of damage to the adhesive bonds used in the joints. Moreover, based on the present optimization results it has been found that the thick adhesive bond will result in higher shear stress transfer with less width and suitable for the lower applied voltage.

Performance Simulation for the Supporting Structure of Aero-Engine Rotor in Wide Frequency Domain

The inertia load of aero-engine indeterminate rotor support is calculated by the finite element method coupled with plane stress element and Fourier ring element. Without considering the dynamic characteristics of rotor’s supporting structure, the test results are error-prone and inefficient. A new method for testing the supporting structure performance of aero-engine rotor in wide frequency domain is proposed. On this basis, the structural model of the casing-support and the structural model of aero-engine rotor are constructed by substructure modelling method. Combining the two sub-models, the semi-physical simulation model of the vibration of the engine rotor’s supporting structure is obtained. By superimposing the additional dynamic stiffness matrix of the casing-supporting structure at the designated DOF position in the overall stiffness matrix of the finite element model of the rotor structure, the overall stiffness matrix of the aero-engine rotor supporting structure is obtained. The effective stiffness matrix can be used to calculate the structural dynamic characteristics of aero-engine rotor supporting structure. Experiments show that the average error of the proposed method is 0.0023 and the number of units is 7.98 e4. The calculation time and storage space are reduced by 310 minutes and 166 GB respectively compared with the performance test method of rotor support based on finite element analysis, which shows that the proposed method is more efficient and accurate.

High performance topology optimization computing platform

One of the most challenging tasks in the construction industry nowadays, is to reduce the material demands and distribute, in the same time, the material among the structural system in the best possible way. Topology optimization is a design procedure that is increasingly used, to generate optimized forms of structures in several engineering fields. The current paper presents the Topology Optimization (TO) module of the High-Performance Optimization Computing Platform (HP-OCP) which focuses on civil engineering problems. More specifically the SIMP method [1] is implemented and the topology optimization problem is solved by using the OC algorithm. The HP-OCP is a platform which evaluates several objective functions, such as the volume of the structure, the compliance etc. and can solve constrained or unconstrained structural optimization problems. The above libraries are developed in C#. The core of the platform is created in such way that it can be integrated with any CAE program that has OAPI, XML or any other type of data exchange format. In the proposed work the structural analysis and design software SAP2000 is used. Theoretical aspects are discussed in order to implement the mathematical formulation in a commercial software. Basic and specific features are applied and representative examples are performed. One of the highlights of the proposed work is that the above module can be used for all kind of finite elements. Benchmark tests are presented with structures that are simulated by 2D plane-stress elements, 3D-solid elements and shell elements. Furthermore, it is independent of the type of the mesh, structured or unstructured, so both examples are presented. In the proposed work a powerful tool for both architects and civil engineers is introduced. The analysis and design of the structures are performed in SAP2000 software, in order to achieve a realistic result that could be a solution for a real-world structure.

Non – Linear Finite Element Analysis of Mild Steel Gusset Plates

Steel gusset plates / gussets are extensively used in metal buildings and play a crucial role in transfer of forces but yet are most neglected in analysis and design. The inelastic behaviour of mild steel gussets is studied assuming that a diagonal member / brace subjected to a tensile force is connected to the gusset. Non-linear finite element analysis of gussets is performed with the help of a finite element software ANSYS by developing a simple model. Four noded plane stress element is used for meshing. The effects of engineering and true stress-strain curves, yield plateau, type of hardening, angle of inclination of the brace and bolt / bolt hole diameter on the in-elastic stress and strain distribution of steel gussets are discussed.

Impact of Integration on Straining Modes and Shear-Locking for Plane Stress Finite Elements

Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectangular as well as square element. It is shown that method of integration has no effect on the straining modes, but it influences the eigenvalues of the bending modes. This effect is intensified by increasing the element aspect ratio, confirming the occurrence of shear locking.