A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.

An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters

This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.

Design Change Model for Effective Scheduling Change Propagation Paths

Changes in requirements may result in the increasing of product development project cost and lead time, therefore, it is important to understand how require- ment changes propagate in the design of complex product systems and be able to select best options to guide design. Currently, a most approach for design change is lack of take the multi-disciplinary coupling relationships and the number of parameters into account integrally. A new design change model is presented to systematically analyze and search change propagation paths. Firstly, a PDS-Be- havior-Structure-based design change model is established to describe requirement changes causing the design change propagation in behavior and structure domains. Secondly, a multi-disciplinary oriented behavior matrix is utilized to support change propagation analysis of complex product systems, and the interaction relationships of the matrix elements are used to obtain an initial set of change paths. Finally, a rough set-based propagation space reducing tool is developed to assist in narrowing change propagation paths by computing the importance of the design change parameters. The proposed new design change model and its associated tools have been demonstrated by the scheduling change propagation paths of high speed train＇s bogie to show its feasibility and effectiveness. This model is not only supportive to response quickly to diversified market requirements, but also helpful to satisfy customer require- ments and reduce product development lead time. The proposed new design change model can be applied in a wide range of engineering systems design with improved efficiency.

Measurement of neutron capture cross section on^(71)Ga at 2.15 and 3.19 MeV and uncertainty propagation and covariance analysis

The cross section values of the^(71)Ga(n,γ)^(72)Ga reaction are measured,which are 9.14±0.81 mb and 5.74±0.50 mb at 2.15 and 3.19 MeV,respectively.The detailed uncertainty propagation and covariance analysis are also given.The^(7)Li(p,n)^(7)Be reaction was used to generate the neutrons,and the neutron flux was normalized using the^(115)In(n,n′)^(115)In^(m)monitor reaction.The measured cross section data are compared with the data available in the EXFOR database,the data obtained using nuclear reaction model codes EMPIRE-3.2 and TALYS-1.95,and also the evaluated nuclear data from ENDF/B-VIII.0 and JEFF-3.1/A.The comparison shows that our result at 3.19 MeV is in good agreement with those of EMPIRE-3.2 and JEFF-3.1/A.Since there are no other measurements available at3.19 MeV,our data could not be compared with literature data at 3.19 MeV,but they are consistent with the cross section values available at 2.98±0.26 and 3.0±0.1 MeV.Our result at 2.15 MeV is slightly higher than the literature value available in EXFOR,evaluated value,and theoretically predicted result.

Experimental analysis of acousto-ultrasonic wave propagation mode in thin plate

in the acousto-ultrasonic technique, a broadband ultrasonic wave is injected onto the surface at one location of the tested plate with the help of a longitudinal transducer and a receiving transducer is coupled to the same surface at another location. Thus, understanding the propagation characteristics of the ultrasonic wave is essential for successful application of the technique. It has been found that the dominant acousto-ultrasonic waves produced experimentally in thin plate are multi-mode Lamb waves. The broadband generation and detection of Lamb waves have been performed in two aluminum plates with different thickness using the acousto-ultrasonic method.

Analysis and comparison between two coupled-mode methods for acoustic propagation in range-dependent waveguides

Two coupled-mode methods, namely DGMCM （Direct-Global-Matrix Coupled- Mode Method） and CCMM （Consistent Coupled-Mode Method）, are analyzed and compared. First, both of these two methods provide two-way solutions, and hence they are accurate models. Second, the series of local vertical modes in DGMCM converges as fast as that in CCMM, whereas DGMCM has a more tolerable requirement of the number of segments than CCMM. Third, these two models obtain the field solution by solving the coupled-mode system with different coefficient matrices, in which the computational effort for the required parameters is almost the same. Finally, DGMCM can handle some problems which are difficult for CCMM, such as in a waveguide with a rough bottom, a line source located right on top of a sloping bot- tom, or in the presence of multiple sources. In DGMCM, closed-form expressions for coupling matrices in a two-layer waveguide are given. In addition, the formulation for the line-source problem in plane geometry is derived to update CCMM.

A variational principle analysis of surface acoustic waves propagating under periodic metal grating with finite thickness

A theoretical method is presented,which analyzes properties of surface acoustic waves propagating on metallic gratings with finite thickness by combining finite element method with variational principle on surface acoustic waves propagating on periodic metal gratings. Based on D.P.Chen and Haus theory,a finite element method is used to investigate the effects of metallic gratings upon the propagation of surface acoustic waves.The coupling-of-modes parameters contributed by mechanical loading are expressed by the matrix derived from the finite element method.Consequently D.P.Chen and Haus theory can also be applied to analyze the properties of surface acoustic waves propagating on metallic gratings with finite thickness and arbitrary shape.Finally,the characteristics of surface acoustic waves propagating under gold and aluminum or silver gratings on a few piezoelectric crystals are studied.Numerical results of the coupling-of-modes parameters of the surface acoustic waves are obtained.

Numerical analysis of 3-D sound propagation in lined ducts with circumferential mode sound sources at inlet

Numerical analysis of three-dimensional sound propagation in soft-soft or soft-hard circular ducts with circumferential and axial modes of sound sources at the inlet has been carried out. In this paper , the numerical method and the samples are offered and the effects of circumferential and axial modes on numerical results are discussed in detail .

An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation

Recently,a new differential discontinuous formulation for conservation laws named the Correction Procedure via Reconstruction(CPR)is developed,which is inspired by several other discontinuous methods such as the discontinuous Galerkin(DG),the spectral volume(SV)/spectral difference(SD)methods.All of them can be unified under the CPR formulation,which is relatively simple to implement due to its finite-difference-like framework.In this paper,a different discontinuous solution space including both polynomial and Fourier basis functions on each element is employed to compute broad-band waves.Free-parameters introduced in the Fourier bases are optimized to minimize both dispersion and dissipation errors through a wave propagation analysis.The optimization procedure is verified with a mesh resolution analysis.Numerical results are presented to demonstrate the performance of the optimized CPR formulation.