Abstract: To cure imperfections such as low accuracy and the lack of ability to nucleate hole in the conventional level set-based topology optimization method, a novel method using a trapezoidal method with discrete design variables is proposed. The proposed method can simultaneously accomplish topology and shape optimization. The finite element method is employed to obtain element properties a...

Purpose. The development of a mathematical model an elastic semi-medium with cylindrical cavity reinforced by shell and plate that reinforces the surface based on finite-element approach. non-stationary dynamic stress-strain state this mechanical system under axisymmetric loads, which depends time as unit Heaviside function was analyzed. solution corresponding static problem obtained. Based obt...

A conservative method of level set type for moving interfaces in divergence free velocity fields is presented. The interface is represented implicitly by the 0.5 level set of a function U being a smeared out Heaviside function, i.e., a function being zero on one side of the interface and one on the other. In a transition layer of finite, constant thickness U goes smoothly from zero to one. The ...

We analyze the existence and stability of stimulus-locked traveling waves in a onedimensional synaptically coupled excitatory neural network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output firing rate of a neuron is taken to be a Heaviside function of activity. Give...

We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synapticweights between populations of neuronswhosemean firin...

Abstract An extended meshfree method is employed in this paper for investigating the dynamic behaviour of cracked plates based on first-order shear deformation theory (FSDT). The FSDT a straightforward formulation with assumption as its name implies, which appropriate relatively thick plates. In study, chosen an alternative to conventional mesh-based methods model plate structures. Among variou...

This paper presents two new analytical equations, the Two Exponent Phenomenological Percolation Equation (TEPPE) and Single (SEPPE) which, for proper choice of parameters, approximate widely used Heaviside Step Function. The plots equations presented in figures this show some, but by no means all, step, ramp, delta, differentiable activation functions that can be obtained using percolation equa...