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Gauss Quadrature and Numerical Integration
Published in Guigen Zhang, Introduction to Integrative Engineering, 2017
Evaluate the following integral by direct integration and by 4-point Gauss quadrature for tetrahedrons. I=∫01∫01−r∫01−r−s(3r2+4s2+7t2+15rs+4st+23rt+17rst+50)drdsdt
Mobile jack-up platforms
Published in White David, Cassidy Mark, Offshore Geotechnical Engineering, 2017
More recently, methods for combining models for geotechnical, structural and environmental load in a consistent manner have been receiving attention. Studies have concentrated on describing the shallow foundation behaviour of spudcans in a plasticity framework and in terms of the forces and displacement on the spudcan footing. This allows direct integration within conventional structural analysis programs, as will be shown in this Section. Displacement-based assessment can therefore be accounted for, with the analysis allowing expansion of the initially developed yield surface.
Effect of Proportioning of Lateral Stiffness in Orthogonal Directions on Seismic Performance of RC Buildings
Published in Journal of Earthquake Engineering, 2022
Payal Gwalani, Yogendra Singh, Humberto Varum
The nonlinearity in columns and shear-walls is modelled using fibre-hinge lumped plasticity model. The columns and shear walls are modelled using elastic linear elements with nonlinearity assumed to be lumped in a fibre hinge. At each hinge location, the cross-section is discretized into a number of fibres, each fibre representing either concrete or steel reinforcement. Such discretization enables interaction of axial force with biaxial bending moments, using direct integration of materials’ stress–strain curves. The plane section is assumed to remain planar after bending. In case of columns, fibre-hinges are assigned at the ends of the elements, at a distance equal to half the plastic hinge length, from the face of the connecting element (from the base, in case of the lowermost columns). The plastic hinge length for columns is taken as half of the maximum cross-sectional dimension, which gives fairly accurate results, even for columns subjected to bidirectional excitation (Rodrigues et al. 2012). In case of shear walls, fibre-hinge is assigned at a distance equal to half the plastic hinge length, from the base. Plastic hinge length for shear walls is obtained from the empirical relation proposed by Priestley, Calvi, and Kowalsky (2007). A uniform strain distribution is assumed in the material fibres over the considered plastic hinge length.
Shock absorption analysis based on the tunnel-soil-surface building interaction system
Published in Journal of Asian Architecture and Building Engineering, 2022
Jun Xie, Long Duan, Yantao Li, Jie Yan, Jingjing Pang, Xu Li, Yueyao Chen
The dynamic solution methods in ABAQUS include modal analysis method and direct integration method (Wang and Zhang 2014). The modal analysis method is suitable for calculating the natural frequency of the structure. When analyzing the nonlinear dynamic response problem, the method of directly integrating the equation of motion must be used. Direct integration methods in ABAQUS mainly include implicit integral algorithm and explicit integral algorithm. Compared with the explicit integral algorithm, the implicit method is more suitable for dynamic analysis with long calculation time. Therefore, we will choose the implicit integration method in this paper. When the time history analysis method is used, the solution of the motion equation of the system is completed by the step-by-step integration method. The dynamic equilibrium equation of the dynamic interaction system between tunnel, soil and surface building is (Zhuang 2006):
A computational model of upper airway respiratory function with muscular coupling
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Olusegun J. Ilegbusi, Don Nadun S. Kuruppumullage, Matthew Schiefer, Kingman P. Strohl
The above governing equations were solved subject to the boundary conditions using ADINA computer code (Bathe 2012). The structural analysis utilized the dynamic implicit scheme with direct integration (Adina 1986). A total of 1,851 and 5,194 finite elements were utilized within the structural and fluid domains respectively. Table 2 summarizes the sample grid-independent results used to select the finite elements in the fluid domain. Specifically, the velocity at a specific location within the laryngeal level was monitored for each set of grids utilized for the three cases considered. The results were found to be essentially invariant beyond the grid mesh consisting of 5,194 in the fluid domain and this grid was thus chosen for the results presented in subsequent Section 2.6. The results for the structural elements were found to be even less sensitive to grid sizes and are not presented for brevity. Each computation required about 150 minutes of CPU time on Intel Core i7 computer with 32 GB of memory.