## 2 Structural Optimization Method with Multiphysical Field Coupling  
### Theoretical Basis of Optimization Method  
Lithium-ion batteries consist of conductor structures and protective casings, with the conductor structures serving as critical functional units within the battery system. These structures primarily include poles, connecting pieces, and tabs, which facilitate electrical connections between the internal and external circuits of the battery through the cells [35,36]. Among these components, the poles typically feature significant design redundancy, whereas the connecting pieces and tabs are subject to spatial constraints, limiting their design flexibility. This limitation directly impacts the safety margins of battery packs under extreme operating conditions [37]. Therefore, a comprehensive understanding of the heat generation and dissipation mechanisms in conductor structures is essential for optimizing their current-carrying capacity. (1) Joule heating effect in conductor structures  
The primary heat source in conductor structures originates from the Joule heating effect, which occurs when an electric current flows through the material [38]. The dynamic response of this process is governed by the following thermodynamic equation [39]:  
\[Q=C_{p}m\Delta T \tag{1}\]  
where \(C_{p}\) is the specific heat capacity of the material, \(m\) is the mass of the material, and \(\Delta T\) is the temperature rise on the conductor structures. (2) Heat generation in conductor structures  
According to [PERSON]'s law, when an electric current passes through a conductor, electrical energy is converted into heat [40]. Under a constant current of \(I\), the heat generated within the conductor structures, denoted as \(Q_{+}\), is linearly proportional to the square of the current; the conductor resistance, \(R\); and the duration of conduction \(t\):  
\[Q_{+}=I^{2}Rt \tag{2}\]  
When considering a time-dependent current \(I(t)\) and temperature-dependent resistance \(R(T)\) under actual operating conditions, the differential expression of Joule heating can be extended to  
\[Q_{+}=\int I(t)^{2}\cdot\rho_{\tau}(T)\cdot\frac{I}{S}dt \tag{3}\]  
where \(\rho_{\tau}(T)\) is the resistivity of the material, \(L\) is the length of the conductor structures, and \(S\) is its cross-sectional area. By combining Equations (1) and (3), the rate of temperature change in the conductor structures can be expressed as  
\[\frac{dT}{dt}=\frac{I(t)^{2}R(T)}{C_{p}(T)m}=\frac{I(t)^{2}\rho_{\tau}(T)\cdot \frac{I}{S}}{C_{p}(T)\rho LS}=\frac{\rho_{\tau}(T)}{C_{p}(T)\rho}\cdot\frac{I( t)^{2}}{S^{2}} \tag{4}\]  
where \(\rho\) is the material density. From Equation (4), it is evident that for a given material, the steady-state temperature rise due to Joule heating is influenced by the current intensity, cross-sectional area of the structural components, and conduction duration. Under fixed current and conduction duration, increasing the cross-sectional area effectively reduces temperature rise. (3) Heat dissipation in conductor structuresThe total heat dissipation \(Q_{-}\) of the conductor structures comprises internal conduction through the connecting components and convective heat exchange with the environment. The dynamic heat transfer model is expressed as [41]  
\[ \begin{array}{l}Q_{-}=\int\left[hS^{*}(T(t)-T_{w}(t))\right]dt\\ =\int\left[h(A_{c}+A_{w})(T(t)-T_{w}(t))\right]dt\end{array}  \tag{5}\]  
where \(h\) is the comprehensive convection-conduction heat transfer coefficient and \(S^{*}\) represents the effective heat dissipation area, including the mechanical contact area \(A_{c}\) (crimp interface) and the welding metallurgical bonding area \(A_{w}\). The transient temperature of the conductor structures is denoted as \(T(t)\), while \(T_{w}(t)\) represents the ambient temperature, which includes the temperature of the conduction path (connecting components) and surrounding air.