Available online at ScienceDirect. Procedia Engineering 150 (2016 )

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1 Available online at ScienceDirect Procedia Engineering 50 (06 ) 8 86 International Conference on Industrial Engineering, ICIE 06 Results of the Study on the Influence of Shell Structures on Their Stability T.P. Kasharina* Platov South-Russian State Polytechnic University (NPI), 3, St. Prosvescheniya, Rostov region, Novocherkassk, 34648, Russian Federation Abstract This article considers the effects of the shape of soil-filled shells on their resistance to internal and external influences, which are based on theoretical studies, including numerical methods and experimental studies, as well as their use as soil-filled elements in retaining installations, deep pits to strengthen bases and foundations, highways, etc. They may also be used as anchor-shells in soil-reinforced structures. The stability of shell structures will be more secure and safe when used as a form of Euler curves without inflection points. The results of numerical modeling of soil-filled shells confirm the need to adjust the existing provisions of the settlement. 06 The Authors. Published by by Elsevier Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of ICIE 06. Peer-review under responsibility of the organizing committee of ICIE 06 Keywords: : stability; deformability; inflection points; soil-filled shells; composite materials; Euler curves; soil reinforcement.. Introduction Shell structure elements are increasingly used in modern construction: soil-filled; soil-reinforced; water-filled, etc. They are made of composite materials (nanomaterials), having the ability to maintain the shape of the construction design through external and internal factors. This allows their use in the construction of: highways; retaining elements; ground arrays fortification; bases and foundations of buildings and structures, etc. We have developed a number of technical solutions for this purpose [-3]. * Corresponding author. Tel.: address: kasharina_tp@mail.ru The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of ICIE 06 doi:0.06/j.proeng

2 8 T.P. Kasharina / Procedia Engineering 50 ( 06 ) 8 86 These structural elements are especially needed upon construction in unfavorable climatic zones: northern areas (frozen ground); regions prone to flooding, prone to subside (muddy soil) and man-made grounds; prone to seismic activity, etc. [4-0].. Main calculation position on soil-filled shell Technical solutions were devised and theoretical, experimental and field studies were conducted under the supervision of the author, which later lead to the creation of recommendations for their use [4-9]. It was also revealed during the course of the study that the shape of shell elements made of composite material affect their reliability and safety, that is: N f( F, p, p, T, t, M, P, P, K) () s max in sh where F s is the shape of the shell structure; p, max p in are the characteristic of the ground and the filling, respectively, N/m 3 ; are the main tensile features of the material; t the term of use of the construction (material); T sh force on the shell, N/m ; P, P internal and external pressures on the shell; K the influence of the environment. When theoretically justifying shell structure parameters we use parametric equations of the lower and upper Euler curves [8-0]. Fig Arrangement of the cross-section of the shell from the curve: stable form of the shell structure In order to define the shape of the cross-section, it is necessary to move the upper curve in relation to the o=lower one in such a way that the starting point of the lower curve ( = 0) and the end point of the upper one ( = ) are on the same vertical. Further, upon arrangement, the starting area of the lower curve is retained. Hence, it is wise to keep the earlier coordinates of the axes for the lower curve and use an independent coordinate system for the upper one, moving the starting coordinates to the other end of the branch. Fig.. Thus, for the lower thread, we use the xoy coordinate system. The parametric equation of the lower curve will be as follows:

3 T.P. Kasharina / Procedia Engineering 50 (06 ) y h[ k sin ] ; () k x h[e (, k) E (, k)], () where x and y are the coordinates of the points of the lower curve, ; h is the distance of the most distant points of the lower curve to the filling surface, ; E( ; k) and E ( ; k) are the elliptic integrals of the first and second kind, respectively; k is the modulus of the elliptic integral (modulus of the curve); is the angle of internal friction of water, filling the shell, in degrees; is the angle between the tangent to the curve and the x- axis, degrees. k ;. The modulus of the curve is represented by the formula: k 4N. (3) h where N is the upper thread tension, kn/m. The values of,,, in the fixation points: y h[ k sin ] ; (4) a a k x a he( a, k) E( a, k) (5) Where a a a. (6) When drawing the outlines of the lower thread with equations (4), (5), the parameter should be given values within 0 a. For k the shape of the lower thread will be a curve of the second kind and for k a curve of the first kind. For the upper thread, we use the xoy coordinate system. The parametric equation of the upper curve will be as follows: y k sin h k (7) h k x E, k E (, k ) E, k E (, k ) k (8)

4 84 T.P. Kasharina / Procedia Engineering 50 ( 06 ) 8 86 where x and y are the coordinates of the points of the upper thread, m; h is the distance of the most distant points of the upper curve to the filling surface, m; E( ; k) and E(; k) are the elliptic integrals of the first and second kind, respectively; k is the modulus of the elliptic integral (modulus of the curve); is the angle between the tangent to the curve and the x axis, in degrees. k, k 4N h 4N, (9) where N is the upper thread tension, kn/m. a a, (0) a a a () Coordinates of the fixation points: y k sin a a h k h k x E, k E (, k) E, k E (, k) a k a a () (3) Considering the geometric meaning of the parameters, it is easy to notice that generally, when the outline of the cross-section at the fixation points have a fraction, a a. The shape of the cross-section of the shell is defined by a set of equations (7), (), (3). It is necessary to add the condition of two threads coupling to these equations, that is, a limiting condition to the fixation point: y y h h (4) a a x x (5) a a Based on the above-mentioned, it is necessary to make an outline of the shell structure as a smooth cross-outline (fig. ) and then the limiting condition: or (6) a a Thus, we obtain an optimal shape for the shell structure, stable for changing external loads, which is necessary in choosing such elements [7-9, 8, 9]. 3. Imitation modeling soil-filled shell The estimate for closed soil-filled shells made of the composite material Unisol 650, obtained using the software Simulation (Solid Works application) using the end element method for the following assumptions: the shell is momentless; the material used is homogenous, as shown in Fig 5 [8-0, 5].

5 T.P. Kasharina / Procedia Engineering 50 (06 ) Fig.. Creating limiting conditions: (a) fixing the lower part of the shell; (b) imitation of the force of gravity acting on the model (9,8 s/m ); (c, d, e) pressure of soil on the shell (,59 kn/m ); (f) contacts with the shell elements Fig. 3. Numerical simulation of soil-filled shell with initial form, defined analytically inclined related to the base at an angle of 80: (a) end element net; (b) tension along the Y-axis. Fig. 4. Numerical simulation of soil-filled shell with initial form, defined analytically inclined related to the base at an angle of 00:(a) end element net; (b) tension along the -axis Fig. 5. Simulation of soil-filled shell with initial form, defined analytically inclined related to the base at an angle of 00: (a) end element net; (b) tension along the Y-axis 4. Conclusion The shape of the shell structure used for construction elements, close to Euler curves but without inflection points, that is, stable, was confirmed as a result of the theoretical and experimental studies.

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