The efficiency of direct integration methods in elastic contact-impact problems

A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.

Structural Reliability Analysis Based on Support Vector Machine and Dual Neural Network Direct Integration Method

Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis.

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.

A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS

A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.

A high order single step-βmethod for nonlinear structural dynamic analysis

A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.

Exact Solutions of the Harry-Dym Equation

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.

Research on Nonlinear Dynamic Characteristics ofStructures Supported on Slide-Limited Friction Base Isolation System

This paper presents a new type of base isolation system, i. e. , slide-limited friction (S-LF) base isolation system . Based on this system, the harmonic and subharmonic periodic response of S-LF subjected to harmonic motions is investigated by using Fourier-Galerkin-Newton (FGN) method with Flo-quet theory. The dynamic response of S-LF subjected to earthquake ground motions is calculated with a high order precision direct integration method, and the numerical results are presented in maximum acceleration response spectra of superstructure and maximum sliding displacement response spectrum form. The comparison of isolating effects of S-LF, pure-friction base isolation system (P-F) and resilient-friction base isolation system (R-FBI) shows that the isolating property of S-LF is superior to those of P-F and R-FBI. Finally, by analyzing an engineering example, it is observed that the distribution of the maximum shear between floors and absolute acceleration of S-LF to earthquake ground motion is very different from that of traditional structures.

Dynamic Response of Mold Oscillator Interacting with Steel Slabs

A mathematical model to show the dynamic response of the mold oscillator was suggested. The model con- sidered a frictional interaction between the mold oscillator and slab as several connected nodes. The governing equation considered the slab as a multi-degree-of-freedom （DoF） system, and included a hysteresis model to describe elastic-plastic behavior of the slab; the mold oscillator was given two DoF by utilizing pressure and displacement experiment data. Simulations indicate that the mold and slab execute various vibrations, and that mold oscillation marks are caused by a stick-and-slip phenomenon during intervals, in which the slab contacting the mold moves downward compared to the other slab （negative strip time）. The slab shows the formation of mold oscillation marks to previous formation criterion equally when the mold velocity is faster than the casting speed about downward. The oscillation mark will grow up over 2 Hz exciting frequency with constant 4 mm stroke in simulations. Finally, the negative strip time was compared to the frictional force, hysteresis variable, and plastic force to investigate formation mechanism of the oscillation marks.