Topology optimization techniques are typically performed on a design domain with pre-determined support conditions to generate efficient structures. Allowing the optimizer to simultaneously design supports and topology offers new design possibilities to achieve improved structural performance and reduce the cost of supports. However, existing simultaneous optimization techniques are limited, with most methods requiring cumbersome procedures to pre-define support conditions, which may not be easy for the end-users. This study presents a new element-based simultaneous optimization method by introducing a layer of elements to the boundaries where supports are allowed, which can be simply implemented in finite element (FE) models. Computational algorithms are developed based on a combination of an optimality criteria (OC) method and the bi-directional evolutionary structural optimization (BESO) technique to determine support locations and the structural topology, respectively. A variety of examples are presented to demonstrate the effectiveness of the new method. It is found that the number, position, and stiffness of supports may significantly influence the structural topology. A support location analysis is used to validate the new method and confirms optimal designs. This study shows that treating element-based support locations as additional design variables can effectively obtain efficient and innovative structural designs. Two 3D examples are presented to demonstrate potential practical applications of the new method.

拓扑优化技术通常在具有预定支撑条件的设计域上执行，以生成有效结构。允许优化器同时设计支撑和拓扑提供了新的设计可能性，以提高结构性能并降低支撑成本。然而，现有的同步优化技术是有限的，大多数方法需要繁琐的程序来预定义支持条件，这对最终用户来说可能并不容易。本研究通过在允许支撑的边界上引入一层元素，提出了一种新的基于元素的同时优化方法，这可以在有限元 (FE) 模型中简单地实现。计算算法是基于优化标准 (OC) 方法和双向进化结构优化 (BESO) 技术的组合开发的，分别用于确定支撑位置和结构拓扑。提供了各种示例来证明新方法的有效性。研究发现，支撑的数量、位置和刚度可能会显着影响结构拓扑。支撑位置分析用于验证新方法并确认最佳设计。这项研究表明，将基于单元的支撑位置作为额外的设计变量可以有效地获得高效和创新的结构设计。提供了两个 3D 示例来演示新方法的潜在实际应用。