Abstract This study presents an original formulation for the co-simulation of multibody systems based on partitioning at interface nodes or joints where motion and loads are exchanged between subsystems. The proposed approach shows improved algorithmic stability compared to existing formulations when implemented in explicit, loose coupling, due to the retention of interface mass on both sides of the partition and the explicit exchange of inertia load contributions along with constraint reactions. The stability properties of the proposed approach are illustrated through benchmark problems. Its effectiveness is further validated in complex mechanical systems, including the structural dynamics of beams and shells and the real-time driver-in-the-loop dynamics of a race car.

Abstract The optimisation of the dynamic behavior of drive systems often involves targeted modifications of the system characteristics. Structural and parametric modifications are used to satisfy the constraints of the dynamic requirements. However, many optimisations are still achieved by intuition or parameter variations, even though more streamlined and easy-to-implement tools such as the eigenvalue perturbation method are available. In this article, the eigenvalue perturbation method in the form of an eigenvalue sensitivity analysis is used to efficiently optimise the dynamic behavior for two different use cases using different optimisation measures. This paper demonstrates how eigenvalue perturbation theory can efficiently optimise drivetrain dynamics by systematically modifying system parameters. Two case studies show how eigenvalue sensitivity analysis achieves targeted frequency shifts to avoid resonances: (1) adapting shaft stiffness and control parameters in a torsional drivetrain, and (2) adjusting structural modifications in a wind turbine bedplate. The study introduces the eigenvector tensor product as a weighting matrix, identifying key parameters for effective redesign. Compared to conventional parameter studies, this method enables precise control over system dynamics with minimal computational effort, making it highly applicable for vibration mitigation and drivetrain optimisation.

Abstract This paper presents the validation of a novel code for the dynamic analysis of flexible multibody systems, which leverages projective geometric algebra for the kinematic description of the system. The theoretical foundations of geometric algebra are introduced briefly. A closed-form solution for the interpolation of motion is derived within the proposed framework and a finite element formulation of geometrically exact beams is developed. The accuracy of this code is assessed by comparing its prediction with those of eight multibody dynamics codes developed by independent researchers. Results are presented for three benchmark problems: the flexible four-bar mechanism, the lateral buckling of a thin beam, and the stability of a rotating shaft. Excellent agreement is found between the predictions of the proposed code and the previously published results, confirming the accuracy of the PGA-based approach. These findings demonstrate the potential of geometric algebra as a robust and elegant basis for the analysis of complex multibody systems.

Abstract We discretise a recently proposed new Lagrangian approach to optimal control problems with dynamics described by force-controlled Euler-Lagrange equations (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are in the form of discrete Lagrangians. We show that the discrete necessary conditions for optimality obtained provide variational integrators for the continuous problem, akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This approach paves the way for the use of variational error analysis to derive the order of convergence of the resulting numerical schemes for both state and costate variables and to apply discrete Noether’s theorem to compute conserved quantities, distinguishing itself from existing geometric approaches. We show for a family of low-order discretisations that the resulting numerical schemes are ‘ doubly-symplectic ’, meaning they yield forced symplectic integrators for the underlying controlled mechanical system and overall symplectic integrators in the state-adjoint space. Multi-body dynamics examples are solved numerically using the new approach. In addition, the new approach is compared to standard direct approaches in terms of computational performance and error convergence. The results highlight the advantages of the new approach, namely, better performance and convergence behaviour of state and costate variables consistent with variational error analysis and automatic preservation of certain first integrals.

Abstract One focus of aviation research in recent years has been the reduction of greenhouse gases through weight savings in aircraft construction, e.g. by using lightweight materials such as CFRP components. Lighter aircraft lead to less fuel consumption, which impacts the global carbon footprint and is an important step towards CO 2 -neutral flying. In order to achieve national climate goals, the environmental impact should already be assessed at the production stage. Most recently, hybrid kinematics consisting of serial kinematics (industrial robots on linear rails) and parallel kinematics (hexapod) mounted to the robot’s end effector, have been studied at Fraunhofer IFAM for the purpose of machining distorted CFRP-components. This work analyzes to which extent the redundant degrees of freedom of such hybrid kinematics can be exploited to determine energetically advantageous poses during machining. Therefore, the inverse kinematics are solved within an Optimal Control Problem (OCP) including the forward kinematics as well as minimizing the system’s energy consumption while following a reference trajectory.

Abstract When overconstrained multibody mechanisms are modeled as rigid body systems, some or all of the reaction forces are non-unique, which may affect other simulation results, making them incorrect. Despite this global ambiguity, unambiguously determinable reactions may be present in the system. For some multibody formulations, methods for checking which reactions are unique and which are non-unique are available. This paper presents a new version of the reaction uniqueness analysis approach based on the divide-and-conquer algorithm. In this method, single- and multi-joint connections are treated in the same way, and the approach does not require additional passes along a binary tree. The uniqueness test may be performed by considering the coefficient matrix (in full or reduced form)—after the main pass of the DCA is finished—by using one of the following numerical methods: rank comparison, QR decomposition, SVD, or nullspace approaches. All of them are considered in this article. The new approach can be applied to a broader class of mechanisms than the DCA-based method developed so far. Moreover, more complex reaction sets may be considered. A spatial parallelogram mechanism with a triple pendulum is studied to illustrate the approach. Furthermore, the proposed method is compared with different approaches to uniqueness analysis in terms of computational efficiency.

Abstract The floating frame of reference formulation (FFRF) is one of the most widely used computational methods for modeling linearly elastic flexible multibody systems. It offers a convenient and computationally efficient approach, particularly the nodal-based framework. An advantage of the FFRF is its ability to directly utilize 3D models created with CAD software and meshed with finite element tools, making it an appealing alternative to beam-element models for studying rotating machinery. However, it is well known that the FFRF is not suitable for rotordynamics applications because it fails to capture centrifugal stiffening. Centrifugal stiffening arises as rotating components, such as discs and blades, experience tensile forces that increase their natural frequencies, effectively enhancing structural stiffness. This study addresses this limitation for systems rotating around a fixed axis of rotation and presents a practical solution. The presented approach introduces an additional stiffness term into the FFRF equations of motion, which we demonstrate is essential for achieving accurate rotordynamics simulations. The significant improvements achieved with this approach over the conventional FFRF are demonstrated using three rotors discretized with 3D solid finite elements.

Abstract This work introduces a novel implicit time integration scheme for simulating deformable materials in multibody systems, leveraging a meshless formulation grounded in bond-based peridynamics. The proposed approach enables robust modeling of large deformations, plasticity, and fracture while circumventing key computational bottlenecks inherent in conventional methods. By reformulating bond forces as compliant constraints within a Differential-Algebraic Equation (DAE) framework, the method eliminates the need for explicit tangent stiffness matrices in implicit integration. Instead, the system is efficiently solved introducing dual variables that represent bond forces and their corresponding constraint Jacobians. The framework is further generalized to accommodate non-smooth dynamics via Measure Differential Inclusions (MDIs), wherein fractured bonds are modeled through complementarity conditions. This advancement significantly improves the treatment of contact between particles compared to traditional peridynamic methods, which often rely on ad hoc repulsive force fields. The resulting dual-primal formulation offers enhanced numerical robustness and efficiency, particularly for problems involving complex fractures and contact interactions, while preserving the meshless flexibility of peridynamics.