Analytical modelling and shape optimization of composite girder with adhesive bondline
More details
Hide details
Cracow University of Technology, Faculty of Civil Engineering Division of Structural Mechanics and Material Mechanics, Cracow, Poland
These authors had equal contribution to this work
Submission date: 2023-10-26
Final revision date: 2023-11-24
Acceptance date: 2023-11-30
Online publication date: 2024-01-26
Publication date: 2024-01-31
Corresponding author
Paweł Szeptyński   

Faculty of Civil Engineering, Cracow University of Technology, Warszawska, 31-155, Krakow, Poland
Journal of Theoretical and Applied Mechanics 2024;62(1):129-142
The paper presents a beam theory for composite girders consisting of two beams joined together with an adhesive layer. The height of the bottom beam is considered variable. The governing equations are suitable for formulation of a shape optimization problem in terms of control theory. The use of Pontryagin’s maximum principle enables finding an optimal solution satisfying necessary optimality conditions. The presented optimization approach allows for including issues which cannot be accounted for by commercial topology optimization software. The introduced theory provides an estimated solution, which is then validated by an analysis of a 3D finite element model.
Büskens C., Pesch H.J., Winderl S., 2001, Real-time solutions of bang-bang and singular optimal control problems, [In:] Online Optimization of Large Scale Systems, Springer-Verlag Berlin Heidelberg GmbH, 129-142.
Clouston P., Schreyer A.C., 2018, Wood-concrete composites: a structurally efficient material option, Civil Engineering Practice, 21, 1, 5-22.
de Vito A.F., Vicente W.M., Xie Y.M., 2023, Topology optimization applied to the core of structural engineered wood product, Structures, 48, 1567-1575.
Decker S.A., Ndiaye A., Brangeon B., Sempey A., Galimard Ph., Pauly M., Lagière Ph., Bos F., 2014, Design of multi-story timber building using mutli-objective particle swarm optimization, Proceedings of the WCTE 2014 – World Conference on Timber Engineering, 2, 10-15.
Dias A., Schänzlin J., Dietsch P., 2018, Design of Timber-Concrete Composite Structures, A state-of-the-art report by COST Action FP1402/WG4.
Goland M., Reissner E., 1944, The stresses in cemented joints, Journal of Applied Mechanics, 11, A17-A27.
Hua H., Hovestadt L., Tang P., 2020, Optimization and prefabrication of timber Voronoi shells, Structural and Multidisciplinary Optimization, 61, 1897-1911.
Jasińska D., Kropiowska D., 2018, The optimal design of an arch girder of variable curvature and stiffness by means of control theory, Mathematical Problems in Engineering, 2018, 1-13.
Jasińska D., Mikulski L., 2019, Strength optimization of structural elements by means of optimal control, MATEC Web of Conferences, 262, 10006.
Kravanja S., Žula T., 2021, Optimization of a single-storey timber building structure, International Journal of Computational Methods and Experimental Measurements, 9, 2, 126-140.
Kwiecień A., 2012, Stiff and flexible adhesives bonding CFRP to masonry substrates - Investigated in pull-off test and Single-Lap test, Archives of Civil and Mechanical Engineering, 12, 2, 228-239.
Mayencourt P., Mueller C., 2019, Structural optimization of cross-laminated timber panels in one-way bending, Structures, 18, 48-59.
Mayencourt P., Mueller C., 2020, Hybrid analytical and computational optimization methodology for structural shaping: Material-efficient mass timber beams, Engineering Structures, 215, 110532.
Mikulski L., Jasińska D., Dąbrowska O., 2022, Structure of optimal control in optimal shaping of the steel arch, Civil and Environmental Engineering Reports, 32, 3, 143-165.
Pech S., Kandler G., Lukacevic M., Füssl J., 2019, Metamodel assisted optimization of glued laminated timber beams by using metaheuristic algorithms, Engineering Applications of Artificial Intelligence, 79, 129-141.
Šilih S., Kravanja S., Premrov M., 2010, Shape and discrete sizing optimization of timber trusses by considering of joint flexibility, Advances in Engineering Software, 41, 2, 286-294.
Śliwa-Wieczorek K., Zając B., Kozik T., 2020, Tests on the mechanical properties of polymers in the aspect of an attempt to determine the parameters of the Mooney-Rivlin hyperelastic model, Civil and Environmental Engineering Reports, 30, 2, 1-14.
Szeptyński P., 2017, Energy-based yield criteria for orthotropic materials, exhibiting strength-differential effect. Specification for sheets under plane stress state, Archives of Metallurgy and Materials, 62, 2, 729-736.
Szeptyński P., 2020, Comparison and experimental verification of simplified one-dimensional linear elastic models of multilayer sandwich beams, Composite Structures, 241, 112088.
Szeptyński P., Mikulski L., 2023, Preliminary optimization technique in the design of steel girders according to Eurocode 3, Archives of Civil Engineering, 69, 1, 71-89.
Villar-García J.R., Vidal-López P., Rodríguez-Robles D., Guaita M., 2019, Cost optimisation of glued laminated timber roof structures using genetic algorithms, Biosystems Engineering, 187, 258-277.
Volkersen O., 1938, Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten, Luftfahrtforschung, 15, 41-47.
Journals System - logo
Scroll to top