The GMT-Consortium Large Earth Finder (G-CLEF) is an echelle spectrograph with precision radial velocity (PRV) capability that will be a first light instrument for the Giant Magellan Telescope (GMT). G-CLEF has a PRV precision goal of 40 cm/sec (10 cm/s for multiple measurements) to enable detection of Earth-like exoplanets in the habitable zones of sun-like stars'. This precision is a primary driver of G-CLEF's structural design. Extreme stability is necessary to minimize image motions at the CCD detectors. Minute changes in temperature, pressure, and acceleration environments cause structural deformations, inducing image motions which degrade PRV precision. The instrument's structural design will ensure that the PRV goal is achieved under the environments G-CLEF will be subjected to as installed on the GMT azimuth platform, including: Millikelvin (0.001 K) thermal soaks and gradients 10 millibar changes in ambient pressure Changes in acceleration due to instrument tip/tilt and telescope slewing Carbon fiber/cyanate composite was selected for the optical bench structure in order to meet performance goals. Low coefficient of thermal expansion (C 1E) and high stiffness-to-weight are key features of the composite optical bench design. Manufacturability and serviceability of the instrument are also drivers of the design. In this paper, we discuss analyses leading to technical choices made to minimize G-CLEF's sensitivity to changing environments. Finite element analysis (FEA) and image motion sensitivity studies were conducted to determine PRV performance under operational environments. We discuss the design of the optical bench structure to optimize stiffness to -weight and minimize deformations due to inertial and pressure effects. We also discuss quasi-kinematic mounting of optical elements and assemblies, and optimization of these to ensure minimal image motion under thermal, pressure, and inertial loads expected during PRV observations.