Serving the Numerical Simulation community since 1989 
Nothing in the formulation and implementation of our Sim Tech is without a proper basis in Numerical Simulation. In fact, references for our Sim Tech are made publicly available. The following is a growing list of research papers, books, and refereed engineering journals related to our Sim Tech.
Simulation Technology References
Methodology of model development in the applied sciences
Barna Szabó and Ivo Babuška, Journal of Computational and Applied Mechanics, Vol. 16, No. 2, (2021), pp. 75-86
DOI: 10.32973/jcam.2021.005
Abstract: The formulation and validation of mathematical models in the applied sciences are largely consistent with the methodology of scientific research programmes (MSRP), however an essential modification is necessary: The domain of calibration has to be defined. The ranking and systematic improvement of mathematical models based on objective criteria are described and illustrated by an example. The methodology outlined in this paper provides a framework for the evolutionary development of a large class of mathematical models.
Finite Element Analysis: Method, Verification and Validation, 2nd Edition
Barna Szabó and Ivo Babuška, John Wiley & Sons, Inc., United Kingdom, 2021. ISBN: 978-1-119-42642-4.
Abstract: The revised and updated second edition of Finite Element Analysis: Method, Verification, and Validation offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules.
Clamped member fatigue characteristics of bolted connections subject to out‐of‐plane loading
Lee W. Zambino and Ani Ural, Wiley Online Library, Engineering Reports, May 2021.
Abstract: In the presence of significant cyclic loading, the design of safe and efficient structural connections requires accurate determination of the clamped member stresses, amongst other considerations. Connections with pretensioned bolts and loading applied parallel to the bolt axis constitute a challenging analysis task that is underrepresented in the literature. To address this, parametric finite element analysis was performed on a representative bolted connection subject to out‐of‐plane loading and comprised of an aluminum member and a pretensioned steel bolt – a typical configuration in the aerospace industry. Of particular interest were the flexural stresses and their contribution to fatigue damage along the member faying surface. The analysis results demonstrated that both the location and magnitude of the stress extrema varied greatly with the geometric and loading parameters considered. To quantify regions most susceptible to fatigue damage, an equivalent stress formulation in conjunction with a critical plane approach was implemented. Contour plots were generated illustrating these regions and regression analysis was performed relating the parametric geometry and load quantities to the maximum equivalent and principal stresses. Regions of greatest fatigue susceptibility were shown to vary both radially and tangentially about the fastener. The data presented are intended to improve both the efficiency and safety of bolted connections.
Formulation of a mathematical model for the prediction of fatigue life in the high cycle regime
Barna Szabó and Ricardo Actis, Vehicle and Automotive Engineering 3, pp. 237-244 , October 2020.
Abstract: Application of the concepts and procedures of verification, validation and uncertainty quantification with reference to a mathematical model formulated for the prediction of the fatigue life of structural and mechanical components in the high cycle regime are described. Such models are used for the formulation of design rules and estimating the probability of fatigue life remaining in support of condition-based maintenance (CBM) decisions.
Validation of Notch Sensitivity Factors
Barna Szabó, Ricardo Actis and David Rusk, ASME Journal of Verification, Validation and Uncertainty Quantification, Volume 4, Issue 1, March 2019.
An end-to-end example of the application of the procedures of verification, validation, and uncertainty quantification (VVUQ) is presented with reference to mathematical models formulated for the prediction of fatigue failure in the high cycle range. A validation metric based on the log likelihood function is defined. It is shown that the functional forms of the notch sensitivity factors proposed by Neuber and Peterson cannot be validated but a revised form can be. Calibration and validation are based on published records of fatigue tests performed on notch-free and notched test coupons fabricated from aluminum alloy and alloy steel sheets.
Predictors of fatigue damage accumulation in the neighborhood of small notches
Barna Szabó, Ricardo Actis and David Rusk, International Journal of Fatigue, Volume 92, Part 1, November 2016, pp. 52-60.
Abstract: The effects of small notches on the predicted fatigue life of mechanical and structural components are examined. It is shown that the classical results of Neuber, Peterson and others can be interpreted to mean integral averages of stresses or strains over small volumes that depend on the solution of a problem of elasticity. This interpretation permits generalization of those results to cases that lie outside of the range of parameters considered in conventional mechanical design. Examples are presented.
Notes on Finite Element Modeling
Barna Szabó, Bulletin for The International Association for Computational Mechanics, No 38, January 2016 pp. 14-15.
Abstract: In the following we consider the practice of finite element modeling in structural engineering, with reference to finite element models of airframes constructed with the purpose to estimate loads carried by the principal structural elements.
Unidirectional fiber-reinforced composite laminae: Homogenization and localization
Barna Szabó, Computers and Mathematics with Applications 70 (2015) 1676–1684.
Abstract: An algorithm for the computation of the homogenized material properties of unidirectional fiber-reinforced laminae is described. The method of extraction is such that superconvergence is realized. It is shown that the homogenized material properties are substantially independent of the number of RVEs. An algorithm for the determination of the micromechanical solution over an RVE (localization) is described and the conditions that predictors of failure initiation must satisfy are stated.
Simulation Governance: An Idea Whose Time Has Come
Barna Szabó, Bulletin for The International Association for Computational Mechanics, No 37, July 2015 pp. 6-8.
Abstract: There are substantial economic incentives to reduce reliance on physical testing and increase reliance on numerical simulation. The reasons for this are obvious: Testing is expensive and time consuming and the results of tests are tied to the specific conditions under which they were performed. Testing without a properly formulated plan about how the results will be interpreted and generalized makes no sense. The main points are discussed in the following.
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Simulation governance: Technical requirements for mechanical design
Barna Szabó and Ricardo Actis, Computer Methods in Applied Mechanics and Engineering, Volumes 249-252, pp. 158-168, 2012. DOI: 10.1016/j.cma.2012.02.008.
Abstract: Simulation governance is discussed from the perspectives of formulation and application of design rules in structural, mechanical and aerospace engineering. The key technical requirements are described in the context of what is variously called validation pyramid, building block method and validation experiment hierarchy and illustrated by an example.
Introduction to Finite Element Analysis: Formulation, Verification and Validation
Barna Szabó and Ivo Babuška, John Wiley & Sons, Inc., United Kingdom, 2011. ISBN 978-0-470-97728-6.
Abstract: When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort.
Singularities in Elliptic Boundary Value Problems and Elasticity and their Connection with Failure Initiation
Yosibash Z. Springer Science+Business Media, LLC 2012 DOI 10.1007/978-1-4614-1508-4.
The p-version of the finite element method
Szabó B., Rank E and Duester A. Chapter 5 in Vol. 1 of Encyclopedia of Computational Mechanics. E. Stein, R. de Borst and T. J. R. Hughes, (editors), John Wiley & Sons, Chichester, 2004.
Comments on the convergence of eigenvalues in the p-version of the finite element method
Szabó B., ESRD Technical Note (2009).
Prediction of Distortion of Airframe Components Made from Aluminum Plates
Nervi S., Szabó B. and Young K.A., AIAA JOURNAL Vol. 47, No. 7, July 2009 pp. 1635–1641.
Abstract: A mathematical model formulated for the prediction of distortion of airframe components manufactured from 7050-T7451 aluminum plates, caused by residual stresses introduced by the manufacturing process of the plate, was tested in validation experiments. The results indicate that distortion in thin gauge parts is caused primarily by machining-induced residual stresses. The residual stresses introduced by the plate manufacturing process, which includes hot rolling, quenching stretching, and aging operations, have a minor effect on distortion, consistent with the predictions based on the mathematical model described herein.
On the role of hierarchic spaces and models in verification and validation
Szabó B. and Actis R., Comput. Methods Appl. Mech. Engrg. 198 (2009) pp. 1273–1280.
Equilibrium of nodal forces in the h- and p-versions of the finite element method
Szabó B. and Actis R., ESRD Technical Note (2008).
Abstract: This note was written in response to questions concerning satisfaction of equilibrium conditions by finite element solutions computed by means of StressCheck. These questions were raised because StressCheck does not report nodal forces, however users experienced with conventional finite element analysis codes are expecting to see evidence of equilibrium based on summation of nodal forces. It is shown that (a) the nodal forces associated with each element are in equilibrium in both the h- and p-versions and (b) satisfaction of the equilibrium of nodal forces is a property of the displacement formulation and is unrelated to the quality or reliability of the finite element solution. The PowerPoint document illustrates the main points of the discussion with an example.
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The effects of residual tensile stresses induced by cold-working a fastener hole
Brot A. and Matias C., Israel Aerospace Industries, ASIP Conference (2007).
Finite Element Analysis
Szabó B. and Babuška I., John Wiley and Sons Inc., New York (1991).
The p-version of the finite element method
Szabó B., Düster A. and Rank E., Encyclopedia of Computational Mechanics, Vol 1, Chapter 5, John Wiley and Sons Inc., New York (2004).
On the importance and uses of feedback information in FEA
Szabó B., Actis R., Applied Numerical Mathematics, Vol 52, pp. 219-234 (2005).
Procedures for the verification and validation of working models for structural shells
Szabó B., Muntges D., Journal of Applied Mechanics, Vol 72, pp. 907-915 (2005).
Quasi-regional mapping for the p-version of the finite element method
Királyfalvi G. and Szabó B., Finite Elements in Analysis and Design, Vol 27, pp. 85-97 (1997).
Hierarchic models for laminated plates and shells
Actis R., Szabó B. and Schwab C., Computational Methods in Applied Mechanics and Engineering, Vol 172, pp. 79-107 (1999).
Adaptive selection of polynomial degrees on a finite element mesh
Bertóti, E. and Szabó B., Int. J. Numer. Methods in Engineering, Vol 42, pp. 561-578 (1998).
Linear models of buckling and stress stiffening
Szabó B. and Királyfalvi G., Computational Methods in Applied Mechanics and Engineering, Vol 171, pp. 43-59 (1999).
Solution of contact problems using hp-version of the finite element method
Páczelt I., Szabó B. and Szabó T., Computers and Mathematics with Applications, Vol 38, pp. 49-69 (1999).
Computation of the amplitude of stress singular terms for cracks and reentrant corners
Szabó B and Babuska I., Fracture Mechanics: Nineteenth Symposium ASTM STP 969. T. A. Cruse, Ed., American Society for Testing and Materials, Philadelphia (1988) 101–124.
The Contour Integral Method for Loaded Cracks
Pereira JP and Duarte CA., Communications in Numerical Methods in Engineering. 22 (2006) 421–432.
Superconvergent computations of flux intensity factors and first derivatives by the FEM
Szabó B. and Yosibash Z., Computational Methods in Applied Mechanics and Engineering, Vol 129, pp. 349-370 (1996).
A note on numerically computed eigenfunctions and generalized stress intensity factors associated with singular points
Yosibash Z. and Szabó B., Engineering Fracture Mechanics, Vol 54, pp. 593-595 (1996).
The p-version of the finite element method compared to an adaptive h-version for the deformation theory of plasticity
Düster A. and Rank E., Computational Methods in Applied Mechanics and Engineering, Vol 190, Number 15, pp. 1925-1935, January 2001.
Abstract: A p-version of the finite element method is applied to the deformation theory of plasticity and the results are compared to a state-of-the-art adaptive h-version. It is demonstrated that even for nonlinear elliptic problems the p-version is a very efficient discretization strategy.
A p-version finite element approach for two- and three-dimensional problems of the J2 flow theory with nonlinear isotropic hardening
Düster A. and Rank E., International Journal for Numerical Methods in Engineering, Vol 53, Issue 1, pp. 49-63, October 2001.
Abstract: In this paper an implementation of a two- and three-dimensional p-version approach to the J2 flow theory with non-linear isotropic hardening for small displacements and small strains is presented. Based on higher-order quadrilateral and hexahedral element formulations, a Newton-Raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non-linear model problem. Curved boundaries are taken care of with the blending function method, allowing an accurate representation of geometry with only a few p-elements. Numerical examples demonstrate, that the p-version supplies efficient and accurate approximations to this class of physically non-linear problems.
Nonlinear limit state analysis of laminated plates by p-version of F.E.M.
Woo K.S., Hong C.H., Lee C.G., Basu P.K.
Abstract: A p-version finite element model based on degenerate shell element is proposed for the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflections and moderate rotations. The material model is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function. The model is also based on extension of equivalent-single layer laminate theory (ESL theory) with shear deformation leading to continuous shear strains at the interface of two layers. The validity of the proposed p-version finite element model is demonstrated through several comparative points of view in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic zone.
High order solid elements for thin-walled structures with applications to linear and nonlinear structural analysis
Rank E., Düster A., Muthler A., Romberg R., European Congress on Computational Methods in Applied Sciences and Engineering, July 2004
Abstract: As an alternative to the well-known and widely used dimensionally reduced formulations for an approximation of thin-walled structures we will investigate in this paper the feasibility of strictly three-dimensional models, using high order elements being coupled to a precise geometric description of the structure. As a key issue, the p-version of the FEM is used, offering a consistent and accurate way to implement solid elements having large aspect ratio (up to a few hundred) and to represent much more general shapes of element surfaces than those available in the usual isoparametric approach. A transition from thin- to thick-walled constructions is thus possible without the necessity to couple models of differing dimensions and without imposing any restrictions on the (three-dimensional) kinematics of the structure. We will demonstrate our results in several numerical examples ranging from a strictly three-dimensional simulation of a building to spring-back analysis in metal forming processes.
P-FEM for a class of pressure/density dependent plasticity models with application to cold isostatic pressing
Frage N., Hartmann S., Holzer S., Rank E., Yosibash Z., Dariel M., German-Israeli Foundation for Scientific Research and Development, June 2006
Abstract: During the past decade, the p-version of the finite element method (FEM) was proven to be a reliable tool for simulating linear problems with many advantages compared to the classical h-version FEM. At the same time, an increasing interest has been observed for computing mechanical processes taking into account more realistic material behavior in geometrically and physically nonlinear situations for which classical h-FEMs may fail.
Control of geometry induced error in hp finite element (FE) simulations
Xue D., Demkowicz L., International Journal of Numerical Analysis and Modeling, Vol 2, Number 3, pp. 283-300, March 2005
Abstract: This paper discusses a general framework for handling curvilinear geometries in high accuracy finite element (FE) simulations, for both elliptic and maxwell problems. Based on the differential manifold concept, the domain is represented as a union of geometrical blocks prescribed with globally compatible, explicit or implicit parameterizations. The idea of parametric H – H(curl) – and H(div) – conforming elements is reviewed, and the concepts of exact geometry elements and isoparametric elements are discussed. Presented numerical examples indicate the necessity of accounting for the geometry error in FE error calculations, especially for the H(curl) problems.
Some aspects of coupling structural models and p-version finite element methods
Rank E., Düster A., Krafczyk M., Rucker M., 1998
Abstract: This paper addresses some questions arising from an integration of coupling structural models and p-version finite element methods. After a brief introduction to the p-version for Reissner-Mindlin plate problems we will consider the modelling of loads or elastic foundations acting only on parts of elements. Furthermore, we will address the question of a posteriori control of the accuracy of the approximation being important for reliable computations. The last part of the paper compares the computational efficiency of the p-version to low order approximations. Finally, it will be motivated why the use of the p-version is expected to be superior in parallel efficiency compared to standard h-version codes.
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