Buckling and wrinkling of thin membranes by using a numerical solver based on multivariate Taylor series

Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature’s thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of n...

Investigation of the effect of buckling initiator on energy absorption of thin-walled circular tubes by using of numerical simulation

Cylindrical thin-walled tubes due to construction and easy installation, high energy absorption capacity are used in the automotive industry as an impact energy absorber. However, the main weakness of cylindrical tubes is in the high initial peak load. Therefore, in this paper, to overcome this weakness, a buckling initiator is used at the top of the tube. This buckling initiator is a steel rod...

A Numerical Integration Method by Using Generalized Series of Functions

NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.

Directions for computing truncated multivariate Taylor series

Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...