## 1 Introduction  
In view of the shortage of land worldwide, especially in metropolitan areas, high-rise building is a prioritized land-efficient architectural form developed more than 100 years ago. High-rise building is the product of the comprehensive application of modern sciences and engineering technologies. Smooth construction and sustainability of this new structural form depends on more accurate calculation theory and method than those for non-high-rise structures in light of that the extrusion of high-rise building into space could be as high as 800 m plus, and slight artefacts could be exaggerated into intractable unpredictability. Since the 21 st century, beam-like structures have achieved overwhelming popularity, such as in high-rise buildings [1; 2], long-span bridges [3; 4], robots and aerospace; however, analysis methods for this form of structure are still those conventional Euler-Bernoulli laws for large deflection beams, which contain implicit integral to hinder general engineering application. An explicit higher-resolution analysis method is expected to tackle the high nonlinearity in high-rise buildings or long bridges. The general theory of elastic deflection is called Elastica. To solve a general problem of elastic large deflection, the equivalent load, deflection and longitudinal displacement can be expressed by an analytic expression of elliptic integrals with free-end rotation angle as parameters [5]; indeed, the results have been reported extensively in the classical works of elastic mechanics [6; 7; 8]. For a cantilever beam subject to point load, the solution to this elastic problem is still an implicit solution with an elliptic integral. In this study, the high-rise building is simplified as a large deformation of a cantilever beam subject to point load at the free end, for example, of a loading extremity, as shown in Figure 1. Given that the traditional analytical methods for solving nonlinear equations such as perturbation [9], methods introduced in [10; 11], Adomian decomposition method [12], and \(\delta\)-expansion method [13], in addition to the elliptical integrals mentioned above, cannot provide accurate, convergent and simple solutions, we aim to derive an explicit and accurate expression for rotation angle \(\theta_{b}\), vertical displacement \(\delta_{v}\) and horizontal displacement \(\delta_{h}\) to minimize the potential unpredictability in the large deformation of the long cantilever-like building. Unlike the perturbation technique, the homotopy analysis method (HAM) is independent of any small/large physical parameters. HAM provides us great freedom to choose equation-type and solution expression of the high order approximation equations. A convergence-control parameter \(h\) is introduced into the series solutions to guarantee the convergence. HAM distinguishes itself from other analytic approaches to be applied to complicated problems with strong nonlinearity [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The Foppl-Von Karman's plate equations were solved by HAM [28; 29]. Especially, the steady-state resonant waves were firstly predicted by the HAM in theory [21; 22; 30; 31], which were then confirmed experimentally [30]. [PERSON] et al. derived an explicit solution to the large deformation of a cantilever beam under point load at the free end with HAM [32]. However, the improficiency of this method is identified to be a low convergence rate due to the step-by-step iteration of solutions of linear differential equations to approximate the exact solutions of complex non-linear differential equations; moreover, it fails to serve explicit solutions of vertical and horizontal displacements for large deformation of the beam. In our previous paper, \"Explicit Solution to Large Deformation Cantilever Beam by Improved Homotopy Analysis Method I: ROTATION ANGLE\", an improved homotopy analysis method (IHAM) was proposed. In IHAM, an auxiliary nonlinear operator \(\varepsilon\) is introduced to improve the convergence rate and extend the convergence range.