Bessmertnyi Y. Deformation and stability of shallow thin-walled conical shells under external pressure and non-homogeneous stress-strain state

The thesis for the scientific degree of a candidate of technical sciences (Doctor of Philosophy) in specialty 05.23.17 “Structural mechanic” (19 – architecture and engineering). – State Higher Educational Establishment “Prydniprovs’ka State Academy of Civil Engineering and Architecture”, Ministry of Education and Science of Ukraine, Dnipro, 2021. An abrupt decrement of load-bearing capacity was noticed in result of study of deformation and stability of thin-walled closed cylindrical shells and this phenomenon was named “static resonance”. The essence of static resonance consists in next. An abrupt decrement of load-bearing capacity with increment of pre-critical displacements happens when variability of non-uniform in circumferential direction SSS coincides or is equal to the variability of first tone of Eigen oscillations of unloaded shell. In this work next factors of non-homogeneous SSS for thin-walled shallow shells are investigated: 1) presence of periodical in circumferential direction discrete border fixation (mobile hinge was changed by immobile hinge) under action of external uniform normal to the surface of shell pressure (task 1); 2) presence of combination of external uniform normal to the surface pressure q and applied in the point force F in case of immobile hinge fixation of shell’s border (task 2); 3) modeling of wind load in form of non-linear distribution in circumferential direction (task 3). An investigation of deformation process and stability of thin-walled shallow shells in case of presence of each factor of non-homogeneous SSS has been conducted by to ways. From one side, a numerical model of thin-walled shallow shell was created using software environment ANSYS and finite element FE SHELL 281 that let obtain a spatial shell model and investigate a variability of non-homogeneity of SSS in circumferential direction. From another side, a row of physical experiments of study of thin-walled shallow conical shell of small scale has been made for task 1 – shell under action of external normal pressure and periodically discrete border fixation. Obtained due to the solving of task 1 results and their analysis approve and improve obtained earlier dependencies for static resonance phenomenon forecasting for than-walled shallow conical shells. Obtained dependency clearly determines the variability of periodically non-homogeneous in circumferential direction SSS of shell that is equal to the half-sum of variability of either first tone of Eigen oscillations of unloaded shell or first tone of bifurcation. Solution was made for linear problem in both cases. Obtained due to the solving of task 2 results and their analysis helped to determine limits influence of point of force application along shell generatrix. Obtained non-linear dependencies “qcr – L/R” clearly determines three main area of force influence on general model of stability loss and deformation process – from slow decrement of load-bearing capacity with wave propagation along all the shell surface to the abrupt decrement of load-bearing capacity with wave localization around point of force application. In general, after analysis of obtained data, the transition from slow to abrupt decrement of load-bearing capacity happens in case when point of force application lays in interval L/R = 0.25 … 0.75. Obtained due to the solving of task 3 results and their analysis helped to create model of wind load that is close to reality that let to forecast the way the shell deformation process happens. In general, shallow thin-walled shells can bear wind calculative loads with large preserve coefficient according to the first and second limit calculation state. Created numerical models let investigate a deformation process and stress-strain state of construction on each state of loading. Due to that it is possible to forecast the dangerous combinations of loads that cause non-homogeneous SSS, and to give recommendations of decrease of influence of factors like periodically discrete border fixation, combination of loads or action of wind load. In addition, such a forecast is possible to do because of solution of linear problems only without a necessity of use of large computational power to solve geometrically non-linear problem of deformation. Key words: shallow thin-walled shells, software ANSYS, non-homogeneous stress-strain state, combined load, wind load, periodically discrete border fixation.