As part of the research colloquium for thesis students and doctoral as well as habiliation candidates, we cordially invite you to a lecture as preparation for the GAMM annual meeting on Tuesday, February 24, 2026 at 10:00 a.m. in deviation from the usual schedule The lecture will take place in room 3516. The title is

"Formulation and verification of multi-point constraints to enforce beam assumptions in volumetric finite element simulations of beams using the example of the Euler-Bernoulli hypothesis"

We look forward to seeing you there!

Abstract

When simulating complex slender structures with finite elements, one can either use a computationally efficient beam model or a more detailed and precise continuum model. The former relies on kinematic and static assumptions that restrict the possible deformations. This leads to a computationally efficient model due to the reduced set of parameters, i.e. the kinematics of the reference axis. While these assumptions allow for a drastic reduction in computational complexity, they also act as kinematic constraints. A beam model inherently satisfies these constraints, but when its results are compared to a more detailed continuum model without constraints, deviations can be observed. In many cases, these deviations remain within acceptable limits, and beam models provide an accurate and efficient representation of the structural behavior. Yet, there are scenarios where the standard kinematic assumptions are ill suited, leading to significant errors.

Although this phenomenon is well known, no method has been developed to quantify the influence of the kinematic assumptions on the local and global structural behavior. Such a method is of great interest because it allows the adequate selection of kinematic and static assumptions for each part of the structure. In order to develop such a method, we want to compare the results of three models: (1) a classical beam model following Euler-Bernoulli hypothesis, (2) a continuum model without additional constraints, serving as a reference solution, (3) a continuum model incorporating multi-point constraints to enforce the assumptions.

Motivated by this, the aim of this talk is to find the correct multi-point constraints that need to be employed in the continuum model to enforce the three kinematic and static assumptions of Euler-Bernoulli hypothesis: (i) plane cross-section remains plane, (ii) cross-section remains perpendicular to the beam's reference axis, (iii) no stresses in thickness direction. Preliminary investigations show that the third assumption can be translated into different multi-point constraints depending on the specific interpretation. Thus, in the talk, we compare different constraint formulations on the basis of several numerical examples. This allows for the verification of the correct multi-point constraints. Since a large number of nonlinear constraints is introduced, an efficient master-slave elimination scheme is employed for their handling [1,2]. This approach reduces computational cost while maintaining accuracy.

[1] Boungard, J. and Wackerfuß, J.: Master-slave elimination scheme for arbitrary smooth nonlinear multi-point constraints. In: Computational Mechanics, 74(5):955-992, 2024

[2] Boungard, J. and Wackerfuß, J.: Extension of constraint methods - identification, elimination and handling of redundant and contradictory multi-point constraints. Submitted.