The housing model is based on Islamic principles, aimed at providing a dwelling and fostering tranquility for families, depending on addressing their fixed and changing needs. Given that the physical structure of housing is the space where family gatherings occur, the adaptability of housing to accommodate the evolving needs of families over time is crucial for achieving sustainability within the family unit. In the meantime, the "expansibility" can be effective in climate stability in addition to social stability by making adaptations or changes in housing components according to the changing needs of residents. Given the high consumption of fossil fuels, designing and constructing residential buildings compatible with the climate is essential to reduce energy consumption. The use of private courtyards in residential units not only provides a foundation for the expansion of building walls but also contributes to the illumination of interior spaces and the regulation of climatic conditions. This research aims to identify the optimal pattern of socially and environmentally expansible housing that aligns with family growth. Thus, the research question emerged in search of a housing model that not only allows for the expansibility of housing components within the courtyard of the apartment but also ensures climatic efficiency. The present article addresses social sustainability in housing by examining the expansibility of its components within the apartment courtyard, while also considering environmental sustainability by measuring the solar radiation received by its expansible walls in the courtyard. The use of both qualitative and quantitative methods to identify the model of socially and environmentally expansible housing has, in the first stage, led to the presentation of expansible patterns A, B, and C within the residential apartment courtyard. Then, based on the quantitative method, the patterns were simulated using EnergyPlus software, leading to the identification of the optimal model. As the main result of this research, by comparing the amount of solar radiation received from the south, east, and west in the cold, moderate, and hot months of the same direction units, the best units in the SW direction belong to building B, in the NE and NW direction belong to building C, in the SE direction It belongs to A and C buildings.
