Operator calculus approach to comparison of elasticity models for modelling of masonry structures

The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions

Cultural heritage assets in Central Asia – Interdisciplinary approach to the complex problem of environmental risk assessment.

Uzbekistan owns more than 7,500 Cultural Heritage (CH) assets and the Republic of Tajikistan has registered a total of 2020 historical and cultural monuments including more than 300 architectural and more than 1000 archaeological sites. Several CH assets have been destroyed from constant negative influence of natural and man-made hazards. The governments have made considerable efforts to comply with its obligations under the UNESCO 1972 Convention. Both territories have a number of concepts for the preservation of architectural heritage. Whereas there is a lack of qualified engineers as well as review and consideration of international developments as well as international practice adoptable to Central Asia CH. This paper presents the findings of the partner’s investigations as well as the concept and objectives for the development of a master’s course in Cultural Heritage Conservation in Central Asia within Erasmus+CBHE project with focus on environmental risk assessment and mitigation (hydrogeology, climate changes, seismic action, etc.) on structures and natural places, documentation and monitoring strategies of structures and landscapes, restoration and conservation strategies and others

Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures

The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions