What would be the most optimal shape for a quadcopter design? I have tried the cross beam design, but the center joint, though epoxied, is extremely prone to shearing off on impact.
There's really no "optimal design" for a quadracopter - there are many good designs, each of which is a compromise between several factors like endurance, performance, flight handling characteristics, and durability.
Your question seems to imply that you want something that's geared toward durability (and probably beginner-friendly flight handling characteristics) since you seem to be worried about things "shearing off on impact", and I'm going to break this to you as gently as I can: No aircraft is designed to crash.
Some designs are better at crashing than others -- in manned aircraft that means they're designed to let the occupants walk away, and in unmanned aircraft it means they're designed for you to put the pieces back together as quickly as possible.
The cross-beam design isn't really built for durability. It's the sport model - light, fast, maneuverable, and often just a little bit unsafe.
You can improve its crashworthiness by designing it to break apart on impact (i.e. rather than trying to beef up the center hub build it so the beams can detach and be easily reattached). This will hopefully reduce the work you have to do after a crash.
As an alternate design though, consider something like the one pictured below:
These full-frame quadracopters are the kind you'll often find at mall kiosks (made out of styrofoam). They're great for beginners because the frame design braces itself and can take substantially more abuse than simple cross-beam designs.
The design also inherently protects the propeller blades from whacking into things when you lose control (and innocent bystanders from whacking into the propeller blades) which is a nice bonus.
This particular example has the motors mounted on a modified cross-beam structure under the copter, but designs where the mounting comes from above & an undercarriage is provided for landing are also out there in the wild. Another option is a frame thick enough that your propeller/motor attachments can come out of the middle of the frame, protecting them further.
From what I understand, you want stability and good crash-worthiness.
For stability, what you want is to drop the CG of the middle section below the plane of the propellers. The lower the CG of the middle part, the more stable your craft will be. Additionally, you would want to lower the control sensitivity of the pitch, roll, and yaw axes.
voretaq7 did a great job covering crash worthiness in my opinion, in addition to protecting the propellers from impact, properly designed shrouds can actually improve the performance of your aircraft as well.
The trick to any crash is to dissipate as much energy as possible. One way, as vortaq mentioned is by designing the copter to break apart. Another way is to absorb the fall with purpose-built mechanisms that absorb energy. These mechanisms are generally refered to as suspensions in cars and motorcycles. A suspension consists of a spring mechanism, and a dampening mechanism. The simple description is that you need a spring to absorb the impact, and a dampener to keep it from bouncing back up. Here are some examples:
Flat carbon fiber rods - good spring force, poor dampening, light weight. Shocks (like from RC cars) - limited spring travel, heavy, good dampening. Foam - properties depend on the type of foam, but generally has good dampening.