Permanent magnet motors have become an important component of industrial production, transportation, and aerospace due to their advantages of high torque density, high power density, high reliability, low losses, and high efficiency. Permanent magnet claw pole motor (PMCPM) is a special type of transverse flux motor which has a higher torque density compared to traditional permanent magnet motors. Due to the absence of winding ends, its axial space utilization is high, and the usage of windings is greatly reduced, reducing the cost and weight of the motor. PMCPM has the advantages of small space, a light weight, a high torque density, a high efficiency, and simple production, which have potential for use in the field of electric vehicles. The double-stator structure design can improve the torque density, efficiency, and radial space utilization of PMCPM, which helps to expand their applications in the field of electric vehicles. This article designs two PMCPM with concentrated winding while different rotor structures (PMCPM1 and PMCPM2) and a three-dimensional finite element method is employed to compare and analyze the performance of PMCPM1 and PMCPM2 and the traditional PMCPM (TPMCPM). Multiphysics analysis is carried out for PMCPM1 and PMCPM2. The stress of the inner and outer stators during interference assembly are analyzed. In this paper, a hybrid material core design is proposed, in which the stator yoke is rolled by silicon steel material and the stator claw pole is pressed by the SMC die method. The multiphysics simulation performance of the PMCPM1 and PMCPM2 with hybrid cores is analyzed.