English
Русский 5-17 p.
A variant of the kinematic method of the theory of limit equilibrium is proposed; massive structural elements are considered, the material of which, in the general case, is anisotropic.
A rigid-plastic model of a deformable solid body is adopted. It is assumed that massive structural ele-ments are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite ele-ments”, ARFE) and have 6 degrees of freedom in three-dimensional space. The process of destruction of the material goes along infinitely thin generalized destruction surfaces (GDS), on which the work of all acting internal force factors (IFF) is taken into account – 9 forces and 9 moments. Bodies made of homogeneous isotropic materials that resist tension and compression in different ways are considered. The strength surfaces in the IFF space are described by the corresponding parametric equations.
Using the equilibrium equation in the Lagrange form and the Mises maximum principle, as well as the proposed parametric equations of the limiting surface, the problem of determining the minimum value of the possible kinematic parameter of the load is reduced to a standard linear programming problem (LP), which is solved using the simplex method.
A rigid-plastic model of a deformable solid body is adopted. It is assumed that massive structural ele-ments are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite ele-ments”, ARFE) and have 6 degrees of freedom in three-dimensional space. The process of destruction of the material goes along infinitely thin generalized destruction surfaces (GDS), on which the work of all acting internal force factors (IFF) is taken into account – 9 forces and 9 moments. Bodies made of homogeneous isotropic materials that resist tension and compression in different ways are considered. The strength surfaces in the IFF space are described by the corresponding parametric equations.
Using the equilibrium equation in the Lagrange form and the Mises maximum principle, as well as the proposed parametric equations of the limiting surface, the problem of determining the minimum value of the possible kinematic parameter of the load is reduced to a standard linear programming problem (LP), which is solved using the simplex method.
[1]. Sibgatullin E.S., Sibgatullin K.E., Novoselov O.G. Method for determining the bearing capacity of massive structural elements. Fundamental Research. 2017. 10-1. P. 51 – 55. (rus.)
[2]. Rabotnov Yu.N. Mechanics of a deformable solid. Moscow: Nauka,, 1988. 712 p. (rus.)
[3]. Sibgatullin K.E., Sibgatullin E.S. Safety Factor of Anisotropic Barsinthe Space of Generalized Forces. Mechanics of Composite Materials. 2017. 52 (6). P. 781 – 788. DOI 10.1007/s11029-017-9629-0
[4]. Sibgatullin K.E., Sibgatullin E.S. The determining of the coefficient of safety of bearing ability of anisotropic bars in the general case of their complex resistance. IOP Conference Series Materials Science and Engineering. 2014. 69, 012041. P. 1 – 5. DOI 10.1088/1757-899X/69/1/012041
[5]. Sibgatullin K.E., Sibgatullin E.S. Estimate of strength of anisotropic bars of arbitrary cross-section in the general case of their combined stress. Mechanics of Solids. 2010. 45 (1). P. 67 – 73. DOI 10.3103/S0025654410010103
[6]. Sibgatullin K.E., Sibgatullin E.S. A technique of analyzing critical forces and moments for isotropic rods of arbitrary cross-section in the general case of their complex resistance. Russian Aeronautics. 2008. 51 (2). P. 126 – 129. DOI 10.3103/S1068799808020049
[7]. Batnidze N.A., Sibgatullin E.S. Study of isotropic shell survivability by the analytical method. Russian Aeronautics. 2013. 56 (2). P. 126 – 130. DOI 10.3103/S1068799813020037
[8]. Islamov K.F., Sibgatullin E.S. Rational reinforcement of a reinforced concrete dome with cutouts. “Bulletin of the Tambov University. Series: Natural and Technical Sciences”. 2006. 11 (4). P. 579 – 582. (rus.)
[9]. Sibgatullin E.S. The alternative fracture criterion for the energy-based theory of strength. Strength of Materials. 2001. 2. P. 28 – 34.
[10]. Teregulov I.G., Sibgatullin E.S., Markin O.A. Limiting state of multilayer composite shells. Mechanics of composite materials. 1988. 4. P. 715 – 720. (rus.)
[11]. Buchholts N.N. Basic course of theoretical mechanics. Part I. Moscow: Nauka, 1972. 468 p. (rus.)
[12]. Kachanov L.M. Fundamentals of the theory of plasticity. Moscow: Nauka,1969. 420 p. (rus.)
[13]. Geniev G.A, Kurbatov A.S. Strength criteria of anisotropic materials with regard for different failure mechanisms. Strength of materials. 1991. 12. P. 2 – 6.
[14]. Mailyan L., Yaziev S., Sabitov L. Et al. Stress-strain state of the "combined tower-reinforced concrete foundation-foundation soil" system for high-rise structure. E3S Web of Conferences: Topical Problems of Green Architecture, Civil and Environmental Engineering, TPACEE 2019, Moscow, 164. Moscow: EDP Sciences, 2020. P. 02035. DOI 10.1051/e3sconf/202016402035
[15]. Izotov V.S., Mukhametrakhimov R.Kh., Sabitov L.S. Experimental research of efficiency of disperse reinforcement of stretched zone of flexural concrete elements. Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture. 2011. 1 (9). P. 78 – 85.
[16]. Karataev O.R., Sabitov L.S., Kashapov N.F. Numerical modeling of joint work of supports made of thin–walled rods of shells of closed profile with precast reinforced concrete foundation in PC Ansys. Bulletin of the Technological University 2018. 21 (12). P. 120 – 123. (rus.)
[2]. Rabotnov Yu.N. Mechanics of a deformable solid. Moscow: Nauka,, 1988. 712 p. (rus.)
[3]. Sibgatullin K.E., Sibgatullin E.S. Safety Factor of Anisotropic Barsinthe Space of Generalized Forces. Mechanics of Composite Materials. 2017. 52 (6). P. 781 – 788. DOI 10.1007/s11029-017-9629-0
[4]. Sibgatullin K.E., Sibgatullin E.S. The determining of the coefficient of safety of bearing ability of anisotropic bars in the general case of their complex resistance. IOP Conference Series Materials Science and Engineering. 2014. 69, 012041. P. 1 – 5. DOI 10.1088/1757-899X/69/1/012041
[5]. Sibgatullin K.E., Sibgatullin E.S. Estimate of strength of anisotropic bars of arbitrary cross-section in the general case of their combined stress. Mechanics of Solids. 2010. 45 (1). P. 67 – 73. DOI 10.3103/S0025654410010103
[6]. Sibgatullin K.E., Sibgatullin E.S. A technique of analyzing critical forces and moments for isotropic rods of arbitrary cross-section in the general case of their complex resistance. Russian Aeronautics. 2008. 51 (2). P. 126 – 129. DOI 10.3103/S1068799808020049
[7]. Batnidze N.A., Sibgatullin E.S. Study of isotropic shell survivability by the analytical method. Russian Aeronautics. 2013. 56 (2). P. 126 – 130. DOI 10.3103/S1068799813020037
[8]. Islamov K.F., Sibgatullin E.S. Rational reinforcement of a reinforced concrete dome with cutouts. “Bulletin of the Tambov University. Series: Natural and Technical Sciences”. 2006. 11 (4). P. 579 – 582. (rus.)
[9]. Sibgatullin E.S. The alternative fracture criterion for the energy-based theory of strength. Strength of Materials. 2001. 2. P. 28 – 34.
[10]. Teregulov I.G., Sibgatullin E.S., Markin O.A. Limiting state of multilayer composite shells. Mechanics of composite materials. 1988. 4. P. 715 – 720. (rus.)
[11]. Buchholts N.N. Basic course of theoretical mechanics. Part I. Moscow: Nauka, 1972. 468 p. (rus.)
[12]. Kachanov L.M. Fundamentals of the theory of plasticity. Moscow: Nauka,1969. 420 p. (rus.)
[13]. Geniev G.A, Kurbatov A.S. Strength criteria of anisotropic materials with regard for different failure mechanisms. Strength of materials. 1991. 12. P. 2 – 6.
[14]. Mailyan L., Yaziev S., Sabitov L. Et al. Stress-strain state of the "combined tower-reinforced concrete foundation-foundation soil" system for high-rise structure. E3S Web of Conferences: Topical Problems of Green Architecture, Civil and Environmental Engineering, TPACEE 2019, Moscow, 164. Moscow: EDP Sciences, 2020. P. 02035. DOI 10.1051/e3sconf/202016402035
[15]. Izotov V.S., Mukhametrakhimov R.Kh., Sabitov L.S. Experimental research of efficiency of disperse reinforcement of stretched zone of flexural concrete elements. Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture. 2011. 1 (9). P. 78 – 85.
[16]. Karataev O.R., Sabitov L.S., Kashapov N.F. Numerical modeling of joint work of supports made of thin–walled rods of shells of closed profile with precast reinforced concrete foundation in PC Ansys. Bulletin of the Technological University 2018. 21 (12). P. 120 – 123. (rus.)
Novoselov O.G., Sabitov L.S., Sibgatullin K.E., Sibgatullin E.S., Klyuev A.S., Klyuev S.V., Shorstova E.S. Method for calculating the strength of massive structural elements in the general case of their stress-strain state (kinematic method). Construction Materials and Products. 2023. 6. (3). P. 5 – 17. https://doi.org/10.58224/2618-7183-2023-6-3-5-17