Thin‐walled composite structures are widely used in weight‐critical applications such as aircraft and spacecraft. However, ensuring the stability of such structures under various load cases remains a key challenge in their design and optimization. For omega‐stringer stiffened panels, the local buckling and postbuckling behavior are investigated using closed‐form analytical solutions. The stiffened panel under consideration consists of the skin plate with eccentrically attached stringer feet along the longitudinal sides of the panel, while the remaining part of the omega‐stringer is modeled by corresponding elastically restrained edges. The computational model is based on energy methods and approximates the postbuckling behavior near the bifurcation point using a simplified plate model. To evaluate the new analysis method, a comparison with the finite element analysis is being drawn. Compared to numerical methods, the present model reduces the computational effort, which is particularly advantageous in the design phase.
We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos. We investigate the application of the stochastic Galerkin method and stochastic collocation techniques to compute unknown coefficient functions of the series. Furthermore, existence and local stability of stationary solutions are discussed for each type of method. We present results of numerical computations in two illustrative examples: a logistic equation and an epidemiological model.
This paper investigates the effects of cube‐shaped neighborhoods in peridynamic theory as an alternative to the traditional spherical neighborhoods. We examine how different neighborhood geometries influence the behavior of various peridynamic formulations, including bond‐based models, state‐based formulations, and correspondence methods. The study reveals that cube‐shaped neighborhoods introduce significant anisotropic effects in standard peridynamic formulations due to directional bias in force calculations. A generalized bond constant is derived for the bond‐based model to maintain consistency with classical continuum mechanics when using cubic neighborhoods. Through numerical examples, including wave propagation and crack growth scenarios, we demonstrate that while cube‐shaped neighborhoods cause undesirable anisotropic behavior in traditional peridynamic models, correspondence‐based formulations remain unaffected due to their averaged deformation gradient approach. The results provide important insights for the selection of neighborhood shapes in peridynamic simulations and highlight the robustness of correspondence formulations against geometric variations in discretization choices.
Quantum computing utilizes the underlying principles of quantum mechanics to perform computations with unmatched performance capabilities. Rather than using classical bits, it operates on qubits, which can exist in superposition and entangled states. This enables the solution of problems that are considered intractable for classical computers. However, since qubits are realized by physical systems such as the spins of electrons, they are highly sensitive to environmental disturbances and hardware imperfections. To achieve reliable scaling and practical application in the future, addressing these errors is of utmost importance. Different classes of errors exist, such as coherent and incoherent errors, caused by imperfections in quantum operations or the decoherence of quantum states. They are inherently different, as they arise from either a lack of precision or intrinsic randomness. Current literature struggles to provide a unified framework that models both types of errors simultaneously. In this paper, an approach based on possibility theory—a theory of imprecise probabilities—is presented to model quantum uncertainty. Possibility theory is particularly useful for systems affected by both epistemic and aleatoric uncertainty, that is, uncertainty due to limited knowledge and uncertainty due to inherent randomness, respectively. By exploring noisy quantum algorithms within a possibilistic framework, different statements about robustness can be derived without requiring prior assumptions about the underlying noise model. Moreover, a possibilistic model enables the derivation of sampling criteria for guaranteed statistical performance and provides insight into the number of measurements required—an important consideration, given that such resources are costly in practice.
This work delves into the advancement of topology optimization techniques for buckling structures that are subject to size limitations. Conventional density‐based methods are prone to yielding intricate, fine‐scale geometries that are challenging to fabricate. To circumvent this challenge, this work imposes constraints on the density distribution and utilizes aggregation techniques to consolidate local volume constraints into a unified global restriction. This approach ensures a more uniform distribution of material throughout the structure, thereby reducing material clustering, avoiding excessively thin layers, and enhancing both the manufacturability and structural performance. Numerical examples are employed to optimize the topology of buckling structures with varying size constraint parameters. The optimization outcomes demonstrate that the proposed methods are capable of effectively achieving optimal topologies that exhibit enhanced stability and strength while adhering to the specified size constraints.
