How Long to Read A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics

How Long Does it Take to Read A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics?

It takes the average reader 2 hours and 30 minutes to read A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics by Matthias C. Schulz

Assuming a reading speed of 250 words per minute. Learn more

Description

The novel finite element formulations fall into the category of geometrically exact Kirchhoff-Love beams. A prominent characteristic of this category is that the absence of shear deformation is strongly enforced by removing two degrees of freedom. Further, the corresponding beam theories exhibit not only translational but also rotational degrees of freedom and their configurations thus form a non-additive and non-commutative space. Sophisticated interpolation schemes are required that need to be tested not only for locking, spatial convergence behavior, and energy conservation, but also for observer invariance and path-independence. For the three novel beam element formulations all these properties are analytically and numerically studied and confirmed, if applicable. Two different rotation parameterization strategies are employed based on the well-known geodesic interpolation used in many Simo-Reissner beams and the lesser known split into the so-called \textit{smallest rotation} and a torsional part. Application of the former parameterization results in a mixed finite element formulation intrinsically free of locking phenomena. Additionally, the first geometrically exact Kirchhoff-Love beam element is presented, which strongly enforces inextensibility by removing another degree of freedom. Furthermore, the numerical efficiency of the new beam formulations is compared to other beam elements that allow for or suppress shear deformation. When modeling very slender beams, the new elements offer distinct numerical advantages. Standard molecular dynamics simulations, which are commonly used to study polymers, suffer from a lack of a careful mathematical basis and the use of an expensive explicit time integration scheme. To circumvent these shortcomings and to be able to simulate stretching experiments on relevant time scales, the problem is described by a stochastic partial differential equation, which can be solved using the finite element method with a backward Euler temporal discretization. In detail, the polymer is represented by a Kirchhoff-Love beam with a linear elastic constitutive model. Inertial and electrostatic forces are neglected. It is deformed by a distributed load mimicking collisions with molecules of the surrounding fluid. Naturally, this load heavily fluctuates over time and space and mean values need to be computed in a Monte Carlo manner. To vastly speed up the fitting process to experimental data in a Bayesian framework, a surrogate model based on a Gaussian process is set up, which directly computes the mean values for given material parameters. The uncertainties and correlations of the material parameters are studied and compared to the literature.

How long is A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics?

A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics by Matthias C. Schulz is 150 pages long, and a total of 37,500 words.

This makes it 51% the length of the average book. It also has 46% more words than the average book.

How Long Does it Take to Read A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 24 minutes to read A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics aloud.

What Reading Level is A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics?

A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics?

A New Kirchhoff-Love Beam Element and its Application to Polymer Mechanics by Matthias C. Schulz is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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