Two Ways of Solving System of Nonlinear Structural Equations

Abstract

By applying the inner product of vectors, two objective functions are found. These vectors are taken from the structural equilibrium path. Via minimizing these functions, with respect to the load incremental parameter and the angle between particular vectors, two new constraint equalities are achieved. Since the scheme of authors is general, three more constraints are also reached. These formulations are similar to the previous presented nonlinear solvers, which confirm the legitimacy of new procedure. Afterward, several numerical tests are performed to prove the ability of the proposed techniques. Findings show that the new algorithms are capable in passing the load and displacement limit points of the various benchmark problems with severe nonlinear behaviors. Based on the number of increments and iterations and also the total analysis duration, the suggested methods have the maximum rapid convergence rate, in comparison to the normal plane, the updated normal plane and the cylindrical arc length strategies.

Mechanical Behavior Analysis of High Strength Concrete Beams in Architectural Design: Simplified Calculation Method of Flexural and Shear Bearing Capacity

“…High-strength concrete, known for its superior compressive strength, enhanced deformation resistance, high density, and reduced porosity, is widely used in large-scale structures such as skyscrapers, expansive bridges, and unique constructions [1][2][3]. Recent advancements have seen the integration of fiber materials into high-strength concrete, significantly improving its tensile strength, compressive strength, elasticity modulus, and durability, while maintaining excellent flowability [4][5][6].…”

Mechanical Analysis of Road Graben Slopes Based on Saturated-Unsaturated Seepage Theory

“…At present, based on rock-saturated-unsaturated seepage theory, Yang Xin used Go-studio finite element software to establish a numerical calculation model for high slopes containing soft and weak inclusions, and carried out a study on seepage characteristics at the top, middle and bottom locations of high slopes containing soft and weak inclusions in road graben under different rainfall factors [3]; Pan H proposed the utility of the Pan H proposed the software of the coupled dynamic mannequin of multi-body gadget in the comparison of action posture stability, mounted the coupled dynamic mannequin of human action posture and accumulated the applicable records of human action posture [4]; Xu Haitao et al used saturation-unsaturation theory to establish a coupled flow-solid model under rainfall infiltration conditions, obtained the distribution of the transient saturation zone and stress field of the cascade slope under different rainfall calendar conditions, and analyzed the damage mechanism of the cascade slope under continuous rainfall conditions, and obtained the corresponding safety factor of the slope [5]; Paul K et al proposed a strong cylindrical gap in a uniform magnetic subject appearing in the route of the axis of the cylindrical gap and the time scheme of the laser beam was once viewed non-Gaussian and acted on the floor of the cylindrical gap [6]; Yu Jinhui picked up the numerical simulation of the seepage characteristics of the high road graben slope under the effect of heavy rainfall by using the finite element calculation software, and obtained the change law of its internal seepage field, based on the principle of effective stress of unsaturated soil and the simplified Bishop method to obtain the change trend of the safety coefficient of the high road slope under the condition of heavy rainfall [7]; The new algorithm proposed via Rezaiee-Pajand M et al is in a position to pass by the load and displacement restriction factors of quite a number benchmark troubles with extreme nonlinear conduct and the proposed technique has the quickest convergence price in contrast to the regular plane, up to date everyday aircraft and cylindrical arc size techniques [8].…”