## 1 Introduction  
To meet the demand for lightweight aircraft, aluminum and titanium alloys as well as fiber-reinforced composites, are commonly used in aircraft manufacturing. Aircraft structures are usually connected by riveted, glued, and glued-riveted joints [1,2]. Rivets are commonly used in aircraft manufacturing because they have high connection strengths, are simple to install, are inexpensive, and produce tight connections [3,4]. Therefore, it is necessary to analyze and evaluate the mechanical properties of riveted joints. A significant amount of research has been conducted to analyze the factors that influence the strengths of riveted joints. [PERSON] et al. [5], [PERSON] [6], and [PERSON] et al. [7] investigated the effects of process parameters on joint strength by using finite element simulations. They found that riveing tool geometry and process parameters affect the riveing strength. [PERSON] et al. [8] investigated the mechanical properties of aluminum alloy rivets and found that the rivet size significantly affects riveted joints. [PERSON] et al. [9] deal with the effects of rivet-hole tolerance in CFRP/Al single-lap blind riveted joints by combining experimental tests and numerical simulation approaches. [PERSON] et al. [10] et al. studied the effect of some controllable process parameters in riveting (i.e., the sequence of the riveting, distance between the rivets (pitch), and the gap between the sheets) on the quality of riveted lap joints and the formed rivets. A good combination of riveting process parameters minimizes the residual stress in sheets and rivets, bulging and material growth in sheets, and reduces the chances of post-riveting clearance in a riveted lap joint. [PERSON] et al. [11; 12] investigated the effect of the edge distance on the strengths of riveted joints, finding that the edge distance significantly affects the dynamic fatigue strength and the static properties of riveted joints. In addition, the shear and peel strengths of the lap specimens increased as the edge distance increased. Since the riveted and bolted lap structures have similar force characteristics, relatively few domestic and foreign scholars have analyzed the load on the riveted construction. Therefore, the load distribution of the riveted lap structure is studied by studying the load distribution of the bolt lap structure. A simplified mechanical model for bolted joints has been developed to study the load distributions in bolted structures. It is assumed that a bolt transmits a load by shear deformation during plate tension or compression, and each bolt is treated as a uniform load [13]. However, the overall strength of a joint can be significantly reduced by the \"short plate effect\" of individual plates; therefore, it is important to quantify this difference when using bolted connections. [PERSON] et al. [14; 15] investigated the effects of fit clearance differences on the stress conditions in bolted members when a load was applied. They measured the magnitude of the load transferred by each bolt, and their results have formed a basis for some scholars to study rivet transfer loads. [PERSON] et al. [16] obtained analytical solutions for the bolt transfer loads at different positions in a plane state by solving the static equilibrium equation and the displacement coordination equation. [PERSON] et al. [17] experimentally investigated the effects of the joint thickness, the laminate taper, and missing fasteners on the load distributions in single-lap multi-bolt joints; they found that missing fasteners can lead to a significant decrease in load-carrying capacity. In summary, most of the analyses of the factors that influence the strengths of riveted joints performed by scholars have focused on the rivet size and the plate thickness. However, the effect of the riveted joint arrangement on the mechanical properties is also significant. Changing the rivet arrangement can effectively improve the mechanical properties of riveted joints [11; 12]; however, little research regarding this topic has been conducted.