Elastic and Thermoelastic Responses of Orthotropic Half-Planes

A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

Nonlinear structures: soliton, shocklike and explosive waves in quantum semiconductor plasma

The properties and conditions for the appearance of some nonlinear waves in a three-dimensional semiconductor plasma are discussed, by studying the described plasma fluid system with quantum gradient forces and degraded pressures. Our analytical procedure is built on the reductive perturbation theory to obtain the Kadomtsev-Petvashvili equation for the fluid model and solving it using the direct integration method and the Bäcklund transform. Through different solution methods we got different nonlinear solutions describing different pulse profiles such as soliton, kink and explosive pulses. This model can be used to identify the potential disturbances in a semiconductor plasma.

Theoretical development of a stiffness decomposition method for calculating the displacement of complex bending structures

It is very difficult to provide analytical displacement solutions for complex bending structures, such as beams with variable cross-sections, in structural analysis. The common methods used for such analysis—the direct integration method and the conventional graph multiplication method—have disadvantages of inefficiency and large computational costs. Therefore, a new approach called the stiffness decomposition method was proposed to overcome these shortcomings. The fundamental principle of this new approach was derived based on the unit load method. The general calculation equation of displacement was derived and provided for general n-segment complex bending structures, and an operational procedure for this method was constructed to facilitate its application. Then, the method was applied to two case studies involving classic complex bending structures. The results showed the correctness and effectiveness of the proposed method. The stiffness decomposition method was simpler and more efficient than the other two methods: the number of computations required by the stiffness decomposition method accounted for only 47.4% to 84.0% of the number of computations required by the other methods in the two case studies. The clear mathematical and mechanical derivation of the proposed method makes it easy to understand. Furthermore, the simplicity and practicality of this method make it extensively applicable.

MODELING OF THE SUBWAY DYNAMIC INFLUANCE ON THE GROUND STRUCTURE

The article discusses a new approach to modeling the behavior of structures under the influence of dynamic loads, including loads from ground and underground transport. The approach is to apply the direct integration method, as well as the SBFEM method to calculate the forces in load-bearing building structures under dynamic influences, taking into account a number of factors - the damping properties of the subgrade, physical nonlinearity of soils and the passage of waves in the soil space. The article presents the main theoretical premises, the results of a numerical experiment of a real monolithic building, built in the zone of influence of the subway.

EFFICIENCY ASSESSMENT OF THE DIRECT INTEGRATION METHOD BY CENTRAL DIFFERENCES (DIMCD)

The direct integration method by central differences (DIMCD) is an explicit method of order two for integrating the equations governing the dynamic analysis of multibody systems. So far, development has focused only on verifying the quality of the results. In this paper, it is shown that in addition to providing optimal results, it is also competitive from the point of view of computational efficiency, at least for systems with up to six bodies. For this purpose, an appropriate implementation of the method in a compiled language is presented. In turn, it is shown that the methodology is suitable for modeling in sparse matrices, although the proposed implementation is based on dense matrices. The resulting code is applied to different benchmark examples. Results from various commercial software are also included. Keywords: Computational efficiency, multibody dynamics, central differences, null space, dense matrices, quaternions

Free vibration and buckling of heavy column with regular polygon cross-section

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

For the calculation of flat shells by the numerical analytical method of boundary elements

The application of the numerical-analytical boundary elements method (NA BEM) to the calculation of shallow shells is considered. The method is based on the analytical construction of the fundamental system of solutions and the Green’s function for the differential equation of the problem under consideration. The theory of calculation of a shallow shell proposed by V. Z. Vlasov, which for the problem under consideration leads to an eighth-order partial differential equation. The problem of bending a shallow shell is two-dimensional, and in the numerical-analytical boundary elements method, the plate and shell are considered in the form of generalized one-dimensional modules, therefore, the Fourier separation method and the Kantorovich-Vlasov variational method were applied to this equation, which made it possible to obtain ordinary differential equations of the eighth order. It is noted that until recently, the main problem in the subsequent implementation of the algorithm of the numerical-analytical boundary element method was due to the fact that all analytical expressions of the method (fundamental functions, Green’s functions, vectors of external loads) are very cumbersome, and intermediate transformations are associated with determinants of the eighth order. It is proposed to use the direct integration method at the first stage, when, along with the original differential equation, an equivalent system of equations for the unknown shell state vector is considered. In this case, the calculations of some analytic expressions associated with determinants of higher orders can be avoided by using the Jacobi formula. As a result, the calculation of the determinant at an arbitrary point is reduced to its calculation at a zero value of the argument, which leads to a significant simplification of all intermediate transformations and analytical expressions of the numerical-analytical boundary elements method.

Buckling of Tapered Heavy Columns with Constant Volume

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

Weakly nonlinear surface gravity waves in a depth-dependent background flow

<p>An open ocean often has a wind driven shear-current near the surface that is able to significantly change the properties of surface waves. This work aims to investigate the effects of a vertically sheared background flow on weakly nonlinear waves with both a statistical study for irregular random waves and a deterministic study for a wave group.</p><p>We first extended the theory by Dalzell (1999) to allow for the effects of a horizontal background flow with arbitrary depth dependence. The extended theory is valid up to second order in wave steepness and is applicable for directional-spread waves of a broad bandwidth. The Direct Integration Method (Li & Ellingsen 2019) is used for the linear dispersion relation.</p><p>Using the theory, we examine the effects of an opposing and assisting shear, respectively, on the nonlinear properties of a short wave group on deep-water through comparisons to cases without a shear flow. A shear flow leads to wave crests (troughs) being either steepened or flattened, depending mainly on the direction of a shear relative to the propagation direction of the group and the strength of the depth-integrated velocity of a shear relative to the group velocity. We, furthermore, investigated skewness and kurtosis of a time record of the wave elevation for irregular waves in a background sheared flow, compared to a linear Gaussian random sea for surface waves only. We obtained the probability density function and exceedance probability for wave crests. Relevance for rogue wave formation is discussed.</p><p><strong>Key words</strong>: waves/free-surface flow, ocean surface waves, wave-current interaction</p><p> </p><p>References</p><p>Dalzell, J. F. "A note on finite depth second-order wave–wave interactions." Applied Ocean Research 21, no. 3 (1999): 105-111.</p><p>Li, Y., and Ellingsen, S. Å. "A framework for modeling linear surface waves on shear currents in slowly varying waters." Journal of Geophysical Research: Oceans 124, no. 4 (2019): 2527-2545.  </p>

Application of viscous dampers for structural response reduction in building renovation

<p>This paper introduces a new idea in the reconstruction and continuation projects. By arranging damping devices, the additional damping of the structure is increased, thereby reducing the dynamic response of the structure under the new seismic precautionary criterion. This paper focuses on the study of viscous dampers which one of the damping device, introduces the energy dissipation principle of viscous dampers, and combines a two-story plane frame case to analyze and compare the dynamic response between non-damping structure and damping structure. The location and quantity of the arrangement were compared with multiple models. Through analysis, it can be seen that by equipping with viscous dampers, seismic energy can be effectively dissipated, thereby reducing the workload of structural reinforcement and having less impact on the original structure. Finally, two commonly analysis methods in damping structures are studied, direct integration method and fast nonlinear analysis (FNA), the main differences between the two analysis methods are introduced, and the calculation results of the two methods are compared and analyzed.</p>