George Papazafeiropoulos

Abaqus2Matlab: A suitable tool for finite element post-processing

Abstract A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage are appropriately described and two problems of particular engineering significance are addressed to demonstrate its capabilities. Firstly, the software is employed to assess cleavage fracture through a novel 3-parameter Weibull probabilistic framework. Then, its potential to create and train neural networks is used to identify damage parameters through a hybrid experimental–numerical scheme, and model crack propagation in structural materials by means of a cohesive zone approach. The source code, detailed documentation and a large number of tutorials can be freely downloaded from www.abaqus2matlab.com .

A generalized algorithm framework for non-linear structural dynamics

The performance of a family of nonlinear generalized single step-single solve (GSSSS) time integration schemes is assessed by comparison of their results in terms of total energy and the agreement with respective results published in the literature. The nonlinear algorithms have been developed by their linear counterparts using a Newton–Raphson iterative procedure to ensure dynamic equilibrium inside each time step. A literature review of the available time integration schemes used for nonlinear problems and the family of linear GSSSS algorithms are presented along with several commonly used time integration algorithms as special cases. Afterwards, the nonlinear schemes are formulated, and outlined in an explicit flowchart, which describes the nonlinear integration procedure in detail. The nonlinear family of algorithms is applied to six benchmark problems involving the dynamic response of SDOF systems with various stiffness and damping properties, as well as to a 3dof structure representing finite element systems containing rigid connections, penalty factors and other such types of constraints. It is shown that the schemes with Continuous Acceleration formulation (such as the HHT-a method) perform in general better than the others, even with a large time step, which leads to reduced computational effort for the estimation of the nonlinear dynamic response with relatively little loss of accuracy.

Pneumatic tyres interacting with deformable terrains

In this study, a numerical model of a deformable tyre interacting with a deformable road has been developed with the use of the finite element code ABAQUS (v. 6.13). Two tyre models with different widths, not necessarily identical to any real industry tyres, have been created purely for research use. The behaviour of these tyres under various vertical loads and different inflation pressures is studied, initially in contact with a rigid surface and then with a deformable terrain. After ensuring that the tyre model gives realistic results in terms of the interaction with a rigid surface, the rolling process of the tyre on a deformable road was studied. The effects of friction coefficient, inflation pressure, rebar orientation and vertical load on the overall performance are reported. Regarding the modelling procedure, a sequence of models were analysed, using the coupling implicit - explicit method. The numerical results reveal that not only there is significant dependence of the final tyre response on the various initial driving parameters, but also special conditions emerge, where the desired response of the tyre results from specific optimum combination of these parameters.

OPTIMUM DESIGN OF CANTILEVER WALLS RETAINING LINEAR ELASTIC BACKFILL BY USE OF GENETIC ALGORITHM

Retaining walls are used in many geotechnical engineering applications, e.g. sup- porting deep excavations, bridge abutments, harbor-quay walls, anchored retaining walls, etc. Although they are generally simple structures, their static and dynamic interaction with the supporting and/or retained soil is a subject of ongoing research. Apart from this, seismic de- sign of retaining walls is primarily based on rules of thumb and the designers experience, in order to set the initial dimensions and make the necessary checks to comply with the design codes. In addition, the calculation of the seismic earth pressures is done in a rather simplistic way which may lead to either conservative or unsafe designs. In the present study, after a comprehensive literature review, optimum design is performed for cantilever walls retaining soil layers of two different heights, using numerical two-dimensional simulations and a genet- ic algorithm. Numerical simulations are performed using the finite element code ABAQUS (1) whereas for optimization purposes, the genetic algorithm provided with MATLAB (2) is uti- lized. For the calculation of the seismic earth pressures, linear elastic soil, retaining wall stem and wall foundation are assumed. The optimization procedure involves four design vari- ables that have to do with the wall geometry, while the soil and wall material parameters and the frequency range of interest are kept fixed. Structural and geotechnical constraints as well as upper and lower bounds for the design variables are imposed to ensure technical feasibil- ity of the solutions. The results on the optimum solutions are presented and comparisons are made with the corresponding results according to conventional seismic design methods. The numerical results of the study provide a clear indication of the direct dynamic interaction be- tween the retaining wall and the surrounding soil, whereas the complexity of the optimization problem itself is evident. This justifies the necessity for a more elaborate consideration of the optimum design of retaining walls, especially if material and geometric non-linearities are taken into account.

A New Energy-Based Structural Design Optimization Concept under Seismic Actions

A new optimization concept is introduced which involves the optimization of nonlinear planar shear buildings by using gradients based on equivalent linear structures, instead of the traditional practice of calculating the gradients from the nonlinear objective function. The optimization problem is formulated as an equivalent linear system of equations in which a target fundamental eigenfrequency and equal dissipated energy distribution within the storeys of the building are the components of the objective function. The concept is applied in a modified Newton-Raphson algorithm in order to find the optimum stiffness distribution of two representative linear or nonlinear MDOF shear buildings, so that the distribution of viscously damped and hysteretically dissipated energy respectively over the structural height is uniform. A number of optimization results are presented in which the effect of the earthquake excitation, the critical modal damping ratio and the normalized yield interstorey drift limit on the optimum stiffness distributions is studied. Structural design based on the proposed approach is more rational and technically feasible compared to other optimization strategies (e.g. uniform ductility concept), whereas it is expected to provide increased protection against global collapse and loss of life during strong earthquake events. Finally, it is proven that the new optimization concept not only reduces running times by as much as 91% compared to the classical optimization algorithms, but also it can be applied in other optimization algorithms which use gradient information to proceed to the optimum point.

OpenSeismoMatlab: A new open-source software for strong ground motion data processing

OpenSeismoMatlab is an innovative open-source software for strong ground motion data processing, written in MATLAB. The software implements an elastoplastic bilinear kinematic hardening constitutive model and uses a state-of-the-art single step single solve time integration algorithm featuring exceptional speed, robustness and accuracy. OpenSeismoMatlab can calculate various time histories and corresponding peak values, Arias intensity and its time history, significant duration, various linear elastic response spectra and constant ductility inelastic response spectra, as well as Fourier amplitude spectrum and mean period. Due to its open-source nature, the software can be easily extended or modified, having high research and educational value for the professional engineering and research community. In the present paper, the structure, algorithms and main routines of the program are explained in detail and the results for various types of spectra of 11 earthquake strong ground motions are calculated and compared to corresponding results from other proprietary software.

Design of RC Sections with Single Reinforcement According to EC2-1-1 and the Rectangular Stress Distribution

Nowadays, the design of concrete structures in Europe is governed by the application of Eurocode 2 (EC2). In particular, EC2—Part 1-1 deals with the general rules and the rules for concrete buildings. An important aspect of the design is specifying the necessary tensile (and compressive, if needed) steel reinforcement required for a Reinforced Concrete (RC) section. In this study we take into account the equivalent rectangular stress distribution for concrete and the bilinear stress-strain relation with a horizontal top branch for steel. This chapter presents three detailed methodologies for the design of rectangular cross sections with tensile reinforcement, covering all concrete classes, from C12/15 up to C90/105. The purpose of the design is to calculate the necessary tensile steel reinforcement. The first methodology provides analytic formulas and an algorithmic procedure that can be easily implemented in any programming language. The second methodology is based on design tables that are provided in Appendix A, requiring less calculations. The third methodology provides again analytic formulas that can replace the use of tables and even be used to reproduce the design tables. Apart from the direct problem, the inverse problem is also addressed, where the steel reinforcement is given and the purpose is to find the maximum bending moment that the section can withstand, given also the value and position of the axial force. For each case analytic relations are extracted in detail with a step-by-step procedure, the relevant assumptions are highlighted and results for four different cross section design examples are presented.

Off-Road Tire-Terrain Interaction: An Analytical Solution

A novel semi-analytical solution has been developed for the calculation of the static and dynamic response of an off road tire interacting with a deformable terrain, which utilizes soil parameters independent of the size of the contact patch (size-independent). The models involved in the solution presented, can be categorized in rigid and/or pneumatic tires, with or without tread pattern. After a concise literature review of related methods, a detailed presentation of the semi-analytical solution is presented, along with assumptions and limitations. A flowchart is provided, showing the main steps of the numerical implementation, and various test cases have been examined, characterized in terms of vertical load, tire dimensions, soil properties, deformability of the tire, and tread pattern. It has been found that the proposed model can qualitatively capture the response of a rolling wheel on deformable terrain.

DEVELOPMENT OF ACCURATE PNEUMATIC TYRE FINITE ELEMENT MODELS BASED ON AN OPTIMISATION PROCEDURE

A novel method for extracting the geometric and constitutive material properties of pneumatic tyres from available numerical or experimental data for the development of realistic and reliable tyre numerical models is proposed. This method involves an optimization procedure, which incorporates a finite element model as a solver (ABAQUS) properly coupled with an optimiser function (MATLAB). Following that, an initial tyre model (P235/75R17) is developed, and then its properties are suitably adjusted via the optimization process, in order for the former to best fit a target model available in the literature, with respect to eigenfre-quency analysis results. After the termination of the algorithm, the “optimum” tyre model (i.e. the model which best conforms to the target model) is obtained, the response of which is further investigated to ensure its realistic behaviour, which warrants its use for various numerical simulations. The results of this study show clearly the efficiency of the optimization procedure proposed, as well as the realistic response of the tyre model developed.

NONLINEAR DYNAMIC RESPONSE OF HARDENING, SOFTENING AND ELASTOPLASTIC SDOF SYSTEMS USING GENERALIZED SINGLE STEP ALGORITHMS WITH NEWTON - RAPHSON ITERATIONS

Abstract. The dynamic equation of motion of a SDOF system with a nonlinear elastic hardening spring, a SDOF system with a nonlinear elastic softening spring and a SDOF system with a nonlinear elastic-plastic spring is integrated numerically using a family of linear generalized single step-single solve algorithms. For this purpose, these algorithms are extended by using a Newton-Raphson type iterative procedure in each time step to ensure dynamic equilibrium. After a literature review of the available time integration schemes used for nonlinear problems, the linear family of algorithms is presented along with several common time integration algorithms as special cases of the generalized algorithm. An explicit flowchart is given showing the integration procedure used in the present study. The modified algorithm is applied to the aforementioned three types of SDOF systems and results concerning phase portraits, (relative) energy decrease, iterations needed for equilibrium and internal force displacement curves are presented. It is shown that the algorithms with optimal numerical dissipation and dispersion perform in general better than others, and that from the algorithms with optimal numerical dissipation and dispersion, only the one with zero-displacement and zero-velocity overshooting behavior can capture efficiently the elastoplastic dynamic response.