scholarly journals A geometrically nonlinear Euler–Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications

2020 ◽  
Vol 8 (4) ◽  
pp. 345-371
Author(s):  
Loc V. Tran ◽  
Jarkko Niiranen
Keyword(s):  
Strain Gradient ◽  
Isogeometric Analysis ◽  
Lattice Structure ◽  
Gradient Elasticity ◽  
Beam Model ◽  
Geometrically Nonlinear ◽  
Strain Gradient Elasticity ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

Zeroth-Order Corrections to the Euler-Bernoulli Beam Model

2010 ◽  
Author(s):  
Harry Dankowicz ◽  
Walter Lacarbonara
Keyword(s):  
Nonlinear Oscillations ◽  
Transverse Motion ◽  
Beam Model ◽  
Geometrically Nonlinear ◽  
Nonlinear Frequency ◽  
Constant Amplitude ◽  
Bernoulli Beam ◽  
Zeroth Order ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

This paper compares the frequency-amplitude relationship for nonlinear oscillations of a geometrically nonlinear model of a slender beam in the absence of damping with the corresponding predictions from the Mettler model for the transverse motion. In particular, the analysis shows that the Mettler model fails to account for a constant, amplitude-independent shift in the nonlinear frequency relative to the linear frequency caused by rotary inertia terms.

scholarly journals Numerical Solution of Bending of the Beam with Given Friction

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 898
Author(s):  
Michaela Bobková ◽  
Lukáš Pospíšil
Keyword(s):  
Sliding Friction ◽  
Quadratic Function ◽  
Building Construction ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Sustainable Building ◽  
Construction Design ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Fixed Beam

We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization problem for finding the coefficients in the finite element basis combines a quadratic function and an additional non-differentiable part with absolute values representing the influence of considered friction. We present two basic algorithms for the solution: the regularized primal solution, where the non-differentiable part is approximated, and the dual formulation. We discuss the disadvantages of the methods on the solution of the academic benchmarks.

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