近几年，深度学习促进了众多领域的发展，由于神经网络具备强大的拟合能力，其在求解偏微分方程取得了前所未有的进步。基于物理信息神经网络（PINN:Physics-Informed Neural Network）是利用神经网络求解偏微分方程的一种数值方法，近几年受到了很大的关注，但是其在求解力学偏微分方程中研究较少。现有的基于最小势能原理的 PINN 能量形式（DEM:Deep Energy Method）没有子域形式，处理交界面的力学问题精度不够，且现有的 DEM 无法应用到实际的复杂结构，缺少基于最小余能原理的 PINN 能量形式。因此本文扩展了现有的深度学习在求解力学偏微分方程的能量形式，来解决复杂的非均匀问题。本文的创新性成果如下：（1）提出了求解复杂边界条件的基于子域 PINN 能量形式的 CENN 算法，扩展了 PINN 能量形式。 CENN 适合处理非均匀物理问题，精度和效率比 DEM 和PINN 子域强形式更高。提出了基于 RBF 径向基函数的可能位移场的构建方法，使得 DEM 可以应用于复杂边界的工程问题。理论上揭示了基于距离函数的可能位移场存在的问题。 CENN 在奇异性，不连续性，高阶张量场，高阶导数以及非线性PDEs 问题进行了验证，证明了 CENN 适合处理交界面问题。此外，本方法不限于求解力学方程，只要是有相应能量形式的物理问题，都可以用该方法根据交界面分布进行子域的分块，提高计算精度。（2）提出了基于最小余能原理 PINN 能量形式的 DCM 算法，与当前 PINN 算法进行了对比，揭示了不同的方法的优劣性。揭示了 DEM 适合处理全力边界条件问题， DCM 适合处理全位移边界条件问题。揭示了不同的方法在不同的应力分量上的精度不同，主要由求导的阶数决定，同时从数值实验上证明计算效率上 DEM和 DCM 要优于 PINN 强形式。提出了增添满足双调和方程的函数项的 DCM-P 算法， DCM-P 算法可以提高 DCM 的精度和收敛速度。理论上提出了基于不同基函数来解决可能位移场在边界条件附近无法学习的可能位移场构建方法。这些研究初步反映了深度学习可以和计算力学相结合的广阔前景，在众多固体力学标准算例进行了验证。结果表明，上述提出的数值方法对于求解固体力学偏微分方程提供了另外一种可能性。此方法独立于有限元，是一种全新的求解固体力学偏微分方程的数值方法。

In recent years, deep learning has promoted the development of many fields. Due to the powerful fitting ability of neural networks, unprecedented progress has been made in solving partial differential equations. Physics-Informed Neural Network (PINN: Physics-Informed Neural Network) is a numerical method for solving partial differential equations using neural networks. The existing PINN energy form (DEM: Deep Energy Method) based on the principle of minimum potential energy has no subdomains form, and the accuracy of dealing with the mechanical problems of the interface is not enough, and the existing DEM cannot be applied to the actual complex structure, and lacks PINN energy form based on the principle of minimum complementary energy. Therefore, this paper extends the existing DEM solving mechanical partial differential equations to solve complex non-uniform problems. The innovative results of this paper is as follows:(1) PINN energy form with subdomains for solving complex boundary conditions call CENN algorithm is proposed, and the PINN energy form is extended. CENN is suitable for dealing with heterogeneous physical problems, and its accuracy and efficiency are higher than DEM and PINN strong forms with subdomains. A construction method of possible displacement field based on RBF radial basis function is proposed, so that DEM can be applied to engineering problems with complex boundaries. We prove there are the inherent problems of possible displacement fields based on distance functions. CENN are validated on singularities, discontinuities, higher-order tensor fields, higher-order derivatives, and nonlinear PDEs, proving that CENNs are suitable for handling interface problems. In addition, this method is not limited to solving mechanical equations. As long as it is a physical problem with a corresponding energy form, this method can be used to divide sub-domains according to the interface to improve the calculation accuracy.(2) A DCM algorithm in the form of PINN energy based on the principle of minimum complementary energy is proposed, which is compared with the current PINN algorithm and reveals the advantages and disadvantages of different methods. It is revealed that DEM is suitable for dealing with full force boundary conditions, and DCM is suitable for dealing with full displacement boundary conditions. It is revealed that different methods have different precisions on different stress components, which are mainly determined by the order of derivation, and numerical experiments prove that DEM and DCM are better than the strong form of PINN in terms of computational efficiency. A DCM-P algorithm is proposed to add function terms that satisfy the biharmonic equation. The DCM-P algorithm can improve the precision and convergence speed of DCM. Theoretically, a possible displacement field construction method based on different basis functions is proposed to solve the problem that the possible displacement field cannot be learned near the boundary conditions.These studies preliminarily reflect the broad prospects that deep learning can be combined with computational mechanics, and have been verified in many benchmarks of solid mechanics. The results show that the numerical method proposed above provides another possibility for solving partial differential equations of solid mechanics. This method is independent of FEM and is a new numerical method for solving solid mechanical partial differential equations.