## 1 Introduction  
Interlaminar stresses can lead to damage in the form of delamination and matrix cracking of laminate, especially at the free-edges of a laminate [1, 2]. Accurate and proper design of bolted composite joints requires the determination of the local stress field within the laminate [3]. Furthermore, the stress field in the vicinity of a bolt hole is generally considered to be three-dimensional (3D) [4, 5, 6]. Thus, it is important to take interlaminar stresses into account in composite bolted joint design. Due to various kinds of bolted composite joints, a filled-hole laminate was used as a means to characterize the stress distribution of bolted joints in this paper. Filled-hole strength has been widely used to generate design data to establish allowables for composite bolted joint analysis [7]. Numerous investigators have studied the stress fields in laminates with a bolt. [PERSON] and [PERSON] [8] presented a review of the previous investigation into the stress and strength analysis of mechanically fastened joints in fiber-reinforced plastics. They concluded that significant issues such as the effects of friction, clearance or interference and the contact area on the stress distribution around a pin-loaded hole. They also suggested that a 3D model was required to accurately predict the strength of mechanically fastened joints. Following that study, [PERSON] [9] developed a 3D finite element model (FEM) of composite bolted joints to determine non-uniform stress distribution through the thickness of laminate in the vicinity of a bolt hole. [PERSON] et al. [10] analyzed the effects of bolt hole clearance on the mechanical behavior of composite bolted joints using a 3D FEM, and studied radial stress through thickness variations at the hole. [PERSON] et al. [11] investigated the influence of stress relaxation on clamp-up load in hybrid composite-to-metal bolted connections by experiment, and the pressure distribution at the free face of the laminate under different clamp-up load was obtained. [PERSON] et al. [12] provided an analysis of the stress distribution at a countersunk hole boundary using the nonlinear finite element code Abaqus. [PERSON] et al. [13] examined the stress distribution among the different bolts by varying the number of rows of bolts as well as the number of bolts per row. The results of their study indicated that in the presence of washers, the stress distributions in the fiber direction and varying fiber inclinations decreased for each value of maximum bearing stresses. [PERSON] et al. [14] proposed a determination method of stress concentration relief factors for failure prediction of composite joints. Moreover, the in-plane stress distribution around the hole edge for open-, filled- and loaded-hole laminates was discussed in their study. These studies were mainly aimed at the investigation of stress distributions at bolt hole edge or in-plane stress distributions. However, the experiments outlined in References [15; 16] have shown that damage might initiate near the edge of the bolt head or washer in composite laminates with bolts. [PERSON] et al. [3] investigated the singular stress fields near the contact surfaces of the bolt head and laminate in a composite bolted joint, and gave all six stress distributions in the position; however, they did not focus on interlaminar stresses. It is also noteworthy that interlaminar stresses are a stress component along the thickness direction of the laminate, therefore, the interlaminar stress distribution along the thickness direction of laminate with a bolt-filled hole should also be investigated. An understanding of geometry-based effects and interlaminar stress distributions are helpful in explaining the failure mode of laminates with a bolt. Several levels of modeling can be used for the evaluation of interlaminar stresses. [PERSON] [17] provided an exact solution for a simply supported plate subject to sinusoidal pressure load, which had been considered a benchmark problem.