By Sergey Aleynikov (auth.)
The publication offers a scientific method of the numeric answer of a vast category of spatial touch challenge in geotechnics. New strategies and effective computing algorithms are thought of at the foundation of the boundary aspect technique – a latest approach to structural mechanics and concept of elasticity. Their useful software permits complex-shaped foundations to be designed with excessive reliability, below spatial rather a lot. a lot recognition is paid to the formula and research of spatial touch types for elastic bases. besides classical schemes of touch deformation, new touch types are mentioned for spatially nonhomogeneous and nonlinearly elastic media, effectively describing the soil homes. The boundary point procedure was once successfully applied in an initially built Rostwerk software program. The boundary point strategies are in comparison with the identified experimental info in addition to with recommendations of comparable difficulties via different equipment and engineering ways.
The proposed boundary aspect approach for fixing spatial touch difficulties is utilized to illustrate the chance for constructing new beginning structures. a brand new method is defined for the selection of the soil deformation modulus, constructed from the answer of a touch challenge for effect of a conical indenter into an elastic half-space.
All the subjects into account are followed through broad calculation facts. the unique effects are complemented via an in depth assessment of the realm literature.
This paintings is meant for the viewers of analysis staff, layout engineers, post-graduate scholars, undergraduates focusing on structural mechanics, concept of elasticity and geotechnics.
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Additional info for Spatial Contact Problems in Geotechnics: Boundary-Element Method
However, the proposed method has not been applied for multilayer bases (with the account of satisfaction of the conjugation conditions at the boundaries of each layer). Besides, no numerical results have been obtained even for a one-layer system, since the representation of the displacement vector components in terms of the Galerkin vector contains unlimited functions. This is an essential inconvenience for the numerical application of the methods, since inadmissibly large numbers appear at high and low values of the Hankel transformation parameters.
It is convenient to characterize the stressed state at each of the nine concentrated forces (three per each layer) by a separate component of the matrix T1x T2x T3x y Q1 y T2 y T3 Q2 T1 Q3 Fig. 4 Elastic Layered Bases 29 where Tk x and Tk y are tangential and Qk are normal concentrated forces on the upper boundary of the k-th layer. 45) where G and ν are the elasticity parameters, εv = ∂U ∂V ∂W + + ; ∂x ∂y ∂z = ∂2 ∂2 ∂2 + + . 47) −∞ ∞ −∞ to Eqs. 45). Taking into account that F ∂ m+n f = ( − iξ )m ( − iη)n f¯ , ∂xm ∂yn one obtains instead of Eqs.
60) 3rd layer: ¯3 ¯ 3 |z=0 = U U z=h2 V¯ 3 |z=0 = V¯ 2 z=h2 or ¯2 ¯ 3 |z=0 = W W σ¯ z(3) S3 |z=0 = S2 z=h2 T3 |z=0 = T2 z=h2 z=h2 , + Q3 = σ¯ z(2) z=h2 , (3) (2) |z=0 + T3x = τ¯xz τ¯xz z=h2 , z=h2 , S3 z=h3 =0 T3 z=h3 = 0, z=0 y (3) (2) |z=0 + T3 = τ¯yz τ¯yz ¯3 U z=h3 =0 V¯ 3 z=h3 =0 ¯3 W or z=h3 , = 0. 61) On the upper boundary of each layer (z = 0), as follows from Eqs. 57), the following conditions are fulfilled: α = σ¯ z |z=0 , β= γ =− E ¯ |z=0 , pW 2( 1 − ν 2 ) E E ¯ + iηV) ¯ |z=0 = − (iξ U S |z=0 , 2 2( 1 − ν ) 2( 1 − ν 2 ) 1 δ = τ |z=0 = − (iξ τ¯xz + iητ¯yz ) |z=0 , p E E ¯ − iξ V) ¯ |z=0 = γ˜ = (iηU T |z=0 , 2( 1 − ν 2 ) 2( 1 − ν 2 ) δ˜ = τ˜ |z=0 = 1 (iητ¯xz − iξ τ¯yz ) |z=0 .