A new 3D-beam finite element including non-uniform torsion with the secondary torsion moment deformation effect

In this paper, a new 3D Timoshenko linear-elastic beam finite element including warping torsion will be presented which is suitable for analysis of spatial structures consisting of constant open and hollow structural section (HSS) beams. The analogy between the 2ndorder beam theory (with axial tension) and torsion (including warping) was used for the formulation of the equations for non-uniform torsion. The secondary torsional moment deformation effect and the shear force effect are included into the local beam finite element stiffness matrix. The warping part of the first derivative of the twist angle was considered as an additional degree of freedom at the finite element nodes. This degree of freedom represents a part of the twist angle curvature caused by the bimoment. Results of the numerical experiments are discussed, compared and evaluated. The importance of the inclusion of warping in stress-deformation analyses of closed-section beams is demostrated

Editorial

„Editorial" Journal of Civil Engineering and Management, 15(1), p. 5-6 First Published Online: 14 Oct 201

Hilltop buckling as the A and O in sensitivity analysis of the initial postbuckling behavior of elastic structures

The coincidence of a bifurcation point with a snap‐through point is called hilltop buckling. In this paper, it either serves as the starting point ‐ the ? ‐ or as the end ‐ the O ‐ in sensitivity analysis of the initial postbuckling behavior of elastic structures. It is shown that hilltop buckling is imperfection sensitive. In sensitivity analyses with hilltop buckling as the starting point (end), the bifurcation point and the snap‐through point are diverging from (converging to) each other. Two classes of sensitivity analyses are identified by means of the consistently linearized eigenproblem. They determine the more (or less) effective mode of conversion of an originally imperfection‐sensitive into an imperfection‐insensitive structure. The results from the numerical investigation corroborate the theoretical findings. The present study is viewed as a step in the direction of better understanding the reasons for different modes of the initial postbuckling behavior of elastic structures and its interplay with the prebuckling behavior. Santrauka Nagrinėjant apkraunamos konstrukcijos elgseną, bifurkacijos taško sutapdinimas su staigaus pasikeitimo tašku vadinamas aukštesniuoju klupumu. Šiame straipsnyje šis taškas yra arba pradžios taškas A, arba proceso pabaigos taškas Ω. Šie taškai imami atliekant tampriųjų konstrukcijų elgsenos jautrumo analizę už pradinio suklupimo ribos. Parodyta, kad aukštesnysis konstrukcijos klupumas priklauso nuo jos geometrinių netikslumų. Kai aukštesniojo klupumo jautrumo analizė sutapdinama su pradiniu tašku, bifurkacijos taškas ir staigaus pasikeitimo taškas artėja vienas prie kito. Identifikuojamos dvi jautrumo analizės klasės sprendžiant nuoseklaus linearizavimo savųjų reikšmių uždavinį. Uždavinio sprendinys lemia daugiau ar mažiau efektyvią klupumo formą, kuri leidžia pakeisti pradinę netikslumams jautrią konstrukciją į konstrukciją, nejautrią jiems. Skaitiniai tyrimai patvirtina teorinius rezultatus. Šie tyrimai padeda nustatant įvairias klupumo formas, nagrinėjant tampriųjų konstrukcijų elgseną už pradinio klupumo ribos ir ryšį su jos elgsena prieš šią ribą. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: nuoseklaus linearizavimo savųjų reikšmių uždavinys, aukštesnysis klupumas, (ne)jautrumas netikslumams, Koiterio analizė už pradinės klupumo ribos, simetrinė bifurkacija, nulinio standumo elgsena už klupumo ribos

International Scientific Networking as an Element of Political Globalization2

The purpose of this paper is to illustrate the importance of international scientific networking as an element of political globalization. The significance of international co­operation in science for universities and academies of sciences is highlighted with special emphasis on the European Research Area. In this context, reference to the role of the Austrian Academy of Sciences is made. 2 Revised version of an article in “VANU on the Road to European Integrations”, Ed. Academy of Sciences and Arts of Vojvodina (VANU), Novi Sad, 2007 by permission of VANU. This article was based on a lecture in Novi Sad, in September 2006.  </p

Displacement-based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameter

This is the peer reviewed version of the following article: Jia, X. and Mang, H. A. (2014), Displacement-based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameter. Proc. Appl. Math. Mech., 14: 195–196, which has been published in final form at https://doi.org/10.1002/pamm.201410085. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The vehicle to investigate to which extent energy‐based categorization of buckling can be linked up with spherical geometry is the so‐called consistently linearized eigenproblem. This investigation requires computation of the first and the second derivative of the tangent stiffness matrix equation image with respect to a dimensionless load parameter λ in the frame of the Finite Element Method (FEM). A finite‐difference approximation of the first derivative of equation image , redefined as a directional derivative, has proved to meet the requirements of computational efficiency and sufficient accuracy. It represents a displacement‐based finite‐difference approximation, abbreviated as DBFDA. The present work is devoted to the computation of a DBFDA of the second derivative of ˜ KT with respect to λ. For the special case of a two‐dimensional co‐rotational beam element, an analytical solution of this derivative is presented. A circular arch, subjected to a vertical point load on its apex, serves as an example for numerically assessing the usefulness of the computed DBFDAs of the first and the second derivative of equation image with respect to λ.Austrian Science Funds (FWF

Mathematical conditions for and physical meaning of a maximum of the determinant of K_T in the prebuckling regime

It is shown that the determinant of the tangent stiffness matrix has a maximum in the prebuckling regime if and only if the determinant of a specific linear combination of the first and the third derivative of this matrix with respect to a dimensionless load factor vanishes. The mathematical tool for this proof is the so-called consistently linearized eigenproblem in the frame of the Finite Element Method. The physical meaning of the mentioned maximum is the one of a minimum of the percentage bending energy of the total strain energy. The paper provides mathematical and physical background knowledge on numerical results that were obtained 35 years ago.Austrian Science Fund (FWF

Determination of the derivative of the tangent stiffness matrix with respect to the load parameter

This is the peer reviewed version of the following article: Jia, X. and Mang, H. A. (2013), Determination of the derivative of the tangent stiffness matrix with respect to the load parameter. Proc. Appl. Math. Mech., 13: 119–120, which has been published in final form at https://doi.org/10.1002/pamm.201310055. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In order to solve the so‐called consistently linearized eigenproblem in the frame of the Finite Element Method (FEM), the derivative of the tangent stiffness matrix equation image with respect to the load parameter λ needs to be calculated. In this work, three schemes for calculation of equation image are presented. The first scheme is based on an analytical expression for the first derivative of e the element tangent stiffness matrix equation image with respect to λ for the special case of a co‐rotational beam element. The second one is a finite difference approach for computation of equation image. The third one is also a finite difference approach. However, it is based on a directional derivative of equation image. An elastic beam, subjected to a compressive axial force and a small transverse uniform load, is chosen as a numerical example. The effectiveness and the accuracy of the three schemes are compared. The third scheme is found to be not only very practical but also more effective than the two competing schemes.Austrian Science Funds (FWF