The high strength-to-weight ratio and ease of manufacturing of composite materials make them widely used across a variety of industries. A commonly used method of improving composite structure load-bearing capacity is to employ carbon fiber-reinforced polymer (CFRP) cores. The mechanical properties of CFRP, however, vary in different directions due to its anisotropic behavior. Due to higher tensile strength along the fibers, anisotropy can lead to failure based on directions other than the fiber orientation. A thorough analysis of CFRP core failure modes has been conducted. Experimental analysis, finite element analysis, and micromechanical modeling techniques have been used in these studies. In this research, specific emphasis has been placed on understanding failure behavior under transverse loading conditions. Failure modes have been thoroughly examined in relation to geometric parameters such as interference, wedge angle, and friction coefficient. Modeling CFRP core failure and displacement behavior was carried out using FEA simulations to validate the research findings. A comparison of the obtained results with existing literature ensured that they were accurate and reliable. Additionally, response surface methodology was employed for optimization, aiming to minimize two critical factors: radial compressive stress and core displacement. By minimizing these factors, the performance and reliability of CFRP cores in applications related to grid capacity can be enhanced. The analysis of the research data revealed that the friction coefficient and interference play significant roles as interacting factors, albeit with opposite impacts on the stresses within the CFRP cores. The optimal values for interference and friction coefficient were found to be 0.0224 mm and 0.4, respectively, to minimize radial stress. Furthermore, the wedge angle exhibited a substantial influence on core displacement, with an optimal value of 3.5°.