We present a novel ground structure-based topology optimization applicable to automotive frame design including joint flexibility. The joint flexibility represents complex and flexible joint responses induced by cross-sectional deformations amplified near a joint. To capture joint flexibility, relevant studies employed one-dimensional higher-order beam theories that consider cross-sectional deformations as additional degrees of freedom. They defined joint matching conditions among kinematic variables through compatibility constraints at joint interface points/lines shared by adjacent members. However, extending these approaches to topology optimization encounters two difficulties: the number and location of joint nodes vary depending on the joint connectivity, and the joint matching conditions represent local matching available only for adjacent two members. To overcome these, Kim et al. defined all possible joint connections as joint types and employed the element stacking method to model joint stiffness variation during topology optimization. However, the approach requires a large number of joint types (e.g., 247 types for a joint connecting eight members), resulting in undesired fluctuations of joint stiffness in situations where a monotonic decrease is expected during topology optimization. Thus, Kim et al. considered ground structures with limited joint connectivity, where only four members are connected to a joint. From these backgrounds, while based on the higher-order beam theory, this study employs new joint matching conditions that can define a fixed joint node regardless of the number of connected members and their joint angles. Additionally, we establish a method for globalizing the local matching conditions involved. Lastly, while incorporating joint flexibility, we eliminate undesired fluctuations and realize joint stiffness variation consistent with classical beam theories during topology optimization. Accordingly, we develop a new ground structure-based topology optimization that not only accurately considers joint flexibility but also has no joint connectivity restrictions.