## 1 Introduction  
The demands for processing complex parts with a free-form surface have resulted in increased use of 5-axis machine tools in automotive, aerospace, die making, and many other industries [1; 2]. The role of the machine tool is to ensure the precise movement relationship between the tool and the workpiece. Meanwhile, the moving parts of machine tools consume large amounts of energy [3]. Therefore, precision and energy consumption are guidelines for machine tool design, and are influenced by many factors including the stiffness error caused by structural deformation, assembly error results in tool position error, system dynamic responses under excitation of operational loads, and so on [4; 5; 6; 7]. In order to reduce energy consumption, lightweight design and optimization techniques are applied to decrease the moving masses and improve the mass-to-payload ratio [8; 9]. Over the last few decades, to improve the accuracy, stiffness, and dynamic performance of machine tools, various lightweight and optimization design methods and strategies have been investigated by many researchers at the early design stage; consequently, structural optimization and lightweight methods have been successfully applied in optimizing dynamical systems and lightweight machines [10; 11; 12; 13; 14; 15; 16; 17; 18]. Lightweight design countermeasures are usually taken through appropriate material selection and implementing a structural optimization method. [PERSON] et al. [12] presented a method using composite-foam-resin concrete sandwich structures instead of metal materials for the lightweight design of micro-EDM machines. [PERSON] et al. [13] reported a stiffness design of machine tool structures based on a biologically inspired topology optimization method, while [PERSON] et al. [14] discussed the general influence of lightweight design approaches on energy efficiency in machine tools, as well as restrictions on the maximum mass reduction for structural components. [PERSON] and [PERSON] [15] reported a design scheme of a lightweight wind turbine tower based on the integration of nanostructured materials produced by a surface mechanical attrition treatment process; the study results revealed that there is sufficient margin for further weight reduction in the traditional wind turbine tower design. In optimization design, [PERSON] et al. [16] proposed an optimization model suitable for press frame designs with respect to energy efficiency. [PERSON] et al. [17] presented an optimization approach for the concept design of machine tools; the results showed that the principal dimensions of all structural parts could be determined while minimizing the weight of the machine and maintaining sufficient stiffness. In order to analyze the dynamic behavior and tool deviations, a dynamic model of a 3-axis gantry milling machine considering axis coupling effects was proposed by [PERSON] et al. [18]. Sandwich structures are commonly used materials for lightweight designs, and their mechanical behaviors are based on their structural features: They are built from two layers, i.e., a stiff and strong skin layer, and a compliant and lightweight core layer [19]. There have been a number of applications in civil and military aircrafts, launch vehicles, wind turbine blades, and marine structures in which composite and sandwich material systems were used as primary structures [20]. Sandwich structures can often sustain large deformations under constant load, enabling them to absorb significant amounts of energy, and to have higher mechanical properties [21; 22; 23; 24; 25; 26; 27]. The structure design methods in existing literatures cannot be directly adapted to the design optimization framework for a large 5-axis machining center (L5 AMC) due to the large dimensions in the \(x\), \(y\), and \(z\) work space and high machining speed.