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Highlights • The new algorithm is the second-order accurate, unconditionally stable (L-stable) and self-starting. • The new algorithm shares the identical effective stiffness matrices inside two sub-steps. • The new method does not involve any artificial parameters and additional variable, such as the Lagrange multipliers. • The new scheme achieves the same numerical properties as the Bathe algorithm, but requires less matrix-vector operations. Abstract This paper presents a new composite sub-steps algorithm for solving reliable numerical responses in structural dynamics. The newly developed algorithm is a two sub-steps, second-order accurate and unconditionally stable implicit algorithm with the same numerical properties as the Bathe algorithm. The detailed analysis of the stability and numerical accuracy is presented for the new algorithm, which shows that its numerical characteristics are identical to those of the Bathe algorithm. Hence, the new sub-steps scheme could be considered as an alternative to the Bathe algorithm. Meanwhile, the new algorithm possesses the following properties: (a) it produces the same accurate solutions as the Bathe algorithm for solving linear and nonlinear problems; (b) it does not involve any artificial parameters and additional variables, such as the Lagrange multipliers; (c) The identical effective stiffness matrices can be obtained inside two sub-steps; (d) it is a self-starting algorithm. Some numerical experiments are given to show the superiority of the new algorithm and the Bathe algorithm over the dissipative CH- α algorithm and the non-dissipative trapezoidal rule. [ABSTRACT FROM AUTHOR]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

Surrogate-models have proven to be an effective strategy for structural systems with expensive-to-evaluate simulations and are very useful for structural reliability analysis. Many kriging model based adaptive sequential sampling methods have been developed recently for efficient reliability analysis. In this paper, a new learning function based on cross-validation is proposed as the guideline to adaptively select new training points at each iteration for reliability analysis. The epistemic uncertainty of the surrogate models and the effects of the aleatory uncertainty of the random variables are considered simultaneously in the proposed new learning function. Three goals can be achieved using the proposed new learning function, i.e., most of the selected new training sample points (1) are selected from the desired regions to improve computational efficiency; (2) reside around the limit-sate functions and in the regions with high reliability sensitivity; and (3) tend to be far away from existing training points in the current design to avoid the clustering problem. The proposed learning function is partly linked to the probability of failure. The proposed method is easy to code and understand as well as implement. Five numerical examples are finally used to validate the accuracy and efficiency as well as applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the existence, uniqueness and asymptotic behaviour of a strong regular solution for a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries: u t - a ∫ Ω t u ( x , t ) dx u xx = f ( x , t ) , ( x , t ) ∈ Q t , u ( α ( t ) , t ) = u ( β ( t ) , t ) = 0 , t > 0 , u ( x , 0 ) = u 0 ( x ) , x ∈ Ω 0 = ] α ( 0 ) , β ( 0 ) [ , where Q t is a bounded non-cylindrical domain defined by Q t = ( x , t ) ∈ R 2 : α ( t ) < x < β ( t ) , for all 0 < t < T . Moreover, we study the properties of the solution and implement a numerical algorithm based on the Moving Finite Element Method (MFEM) with polynomial approximations of any degree, to solve this class of problems. Some numerical tests are investigated to evaluate the performance of our Matlab code based on the MFEM and illustrate the exponential decay of the solution. [ABSTRACT FROM AUTHOR]

In this paper, a new numerical algorithm to solve the linear and nonlinear fractional differential equations (FDE) is introduced. Fractional calculus and fractional differential equations have many applications in physics, chemistry, engineering, finance, and other sciences. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, which is convergent for any x ∈ R. In this method, we reduce the solution of a nonlinear fractional problem to the solution of a system of the nonlinear algebraic equations. To illustrate the reliability of this method, we solve some important equations of fractional order, and present numerical results of the present method to show convergence rate, applicability and reliability of this method. [ABSTRACT FROM AUTHOR]