Shear-Deformable Multi-Scale Homogenized Models

Structures made of functionally graded porous materials have large shear deformation and require appropriate higher-order shear deformation theories to analyze their response. The theories can be re-formulated to allow easier use of PDE solvers.


Keleshteri, M.M., Jelovica, J. “Beam Theory Reformulation to Implement Various Boundary Conditions for Generalized Differential Quadrature Method”. Engineering Structures, Vol. 252, 2022,

Keleshteri, M.M., Jelovica, J. “Nonlinear Vibration Analysis of Bidirectional Porous Beams”. Engineering with Computers, 2021.

Romanoff, J., Reddy, J.N., Jelovica, J. “Using Non-Local Timoshenko Beam Theories for Prediction of Micro- and Macro-Structural Responses”, Composite Structures, vol. 156, pp. 410-420, 2016,

Failure of sandwich structures can consist of several stages, starting at certain scale and progressing towards another. We are modifying equivalent single-layer (ESL) theories to predict such scenarios by defining nonlinear stiffness matrices that are used to define the structure.


Goncalves, B.R., Jelovica, J., Romanoff, J. “A homogenization method for geometric nonlinear analysis of sandwich structures with initial imperfections”, International Journal of Solids and Structures, vol. 87, no. 1, pp. 194–205, 2016.,

As further development of the topic above, nonlinear stiffness of ESL plate theory is extended to include material nonlinearity, and applied to other structures and other loading conditions. In certain scenarios, in-plane shear coupling might be important in predicting the ultimate strength.


Putranto, T., Kõrgesaar, M., Jelovica, J., Tabri, K., Naar, H. “Ultimate strength assessment of stiffened panel under uni-axial compression with non-linear equivalent single layer approach”. Marine Structures, Vol. 78, 2021,

Putranto, T., Kõrgesaar, M., Jelovica, J. “Ultimate strength assessment of stiffened panels using equivalent single layer approach under combined in-plane compression and shear”. Submitted for review.