Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

E. Shivanian, M. Ansari Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

Received: August 21, 2018; in final form January 10, 2019

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In current work, a novel intelligent computational technique is adopted for searching the behaviour of the problem of buckling of nano-actuators in the presence of various nonlinear forces. In order to accomplish this aim, the governing integro-differential equation in general form is taken into account for nano-actuators, which contains various nonlinear forces as well. This generalized form for the nano-actuators is in fact a non-linear fourth-order Fredholm integro-differential boundary value problem. The boundary value problem is transformed into an equivalent problem whose boundary conditions are such that it is convenient to apply reformed version of the Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an uninspected error which is minimized through adjusting weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. This numerical technique enables us to overcome all kind of nonlinearities in the mentioned boundary value problem, and then to obtain an accurate solution. Thus, it can expedite the design of nano-actuators.

DOI:10.12693/APhysPolA.135.444 topics: nano-actuator, Chebyshev polynomial of the first kind, interior point method, Fredholm integral equation